There are several ways in which the believers can become a cause of trial for the disbelievers, for which every believer should seek Allah's refuge. For example,
(1) the disbelievers may gain in upper hand over them and consider it a proof of their being in the right and the believers being in the wrong; otherwise it could not be that in spite of Allah's good pleasure that they claim to enjoy, the disbelievers would have been able to gain an upper hand over them;
(2) the persecution of the believers by the disbelievers may become unbearable with the result that they may yield to them and abandon their Faith and moral values this would subject the believers to public ridicule and would provide the disbelievers with an opportunity to humiliate and debase than and their religion:
(3) in spite of being the standard-bearers of the true Faith the believers may lose their moral superiority that should accrue to them as believers. and the people have the same defects and deficiencies in their character as are commonly found in an un-Islamic community: this would give the disbelievers an opportunity to say that the Faith of the believers was in no way superior to their disbelief. (For further details sec verse 85 of Surah 10. Yunus - reproduced herein under):
(10:85) They replied: 'We place our reliance on Allah. Our Lord! Do not make us a trial for the oppressors,
Those, who responded to the appeal of Prophet Moses (peace be upon him) were those youth who obeyed and followed him, and not the Israelites, as a community, as is obvious from the context.
The prayer, “Our Lord, do not make us a trial for the wrongdoing people” is very comprehensive in meaning. Whenever the standard bearers of the truth rise up to establish virtue and eradicate the prevalent evil, they come into conflict with unjust people, who, for one reason or the other, are always on the lookout to find fault with them. First, there are the champions of falsehood, who try their level best to crush down with full force the champions of the truth. Then there are the so called champions of the truth who profess to believe in it but are not prepared to enter into conflict with the powerful government of the time. Therefore they declare it to be a useless and foolish effort, and begin to invent excuses to justify the wrong stand they take in regard to the struggle with falsehood in order to silence the prick of conscience they feel for their criminal attitude of cowardice. Accordingly, they try to prove that it is these standard bearers of the truth who are in the wrong and not them. Lastly, there are the common people, who watch the conflict as bystanders and join forces with those who prove to be more powerful of the two, whether they are the supporters of the truth or of falsehood.
Now let us consider how the champions of the truth are liable to become a cause of trial for these unjust people. If they are crushed down or defeated, the first group declares, we were in the right and not these foolish people: otherwise they could not have been defeated. The second group says, their defeat has proved that they did not make the correct estimate of the circumstances and caused the destruction of valuable lives by coming in conflict with the mighty powers. Moreover, the Shariat has not made it obligatory on us to expose ourselves to risk, when we are fulfilling the most essential religious duties without any restrictions from the tyrants of the day. As regards to the common people, their criterion of judging the truth is this: Whatever triumphs is truth. Therefore their defeat has proved that the champions of the truth must be in the wrong. Likewise, every mistake and error the champions of the truth commit, every weakness they show in the face of overwhelming odds against them, every moral fault to which anyone of them succumbs, becomes a good excuse for those who intend to stick to falsehood. Consequently, the invitation to the truth becomes dormant for years after their defeat.
Thus it has become quite clear that this prayer of the companions of Prophet Moses (peace be upon him) was well timed and meaningful: Our Lord, have mercy upon us so that we might not become a cause of trial for the unjust people: protect us from errors, defects and, weaknesses and make our efforts successful in this world so that we may become a source of goodness to Thy creatures and not a source of evil for the unjust people.
Tafsir Ibn-Kathir: (Our Lord! Make us not a trial for the disbelievers,) Mujahid said, "It means, `Do not punish us by their hands, nor with a punishment from You.' Or they will say, `Had these people been following the truth, the torment would not have struck them'.'' Ad-Dahhak said something similar. Qatadah said, "Do not give the disbelievers victory over us, thus subjecting us to trials by their hands. Surely, if You do so, they would then think that they were given victory over us because they are on the truth.'' This is the meaning that Ibn Jarir preferred. `Ali bin Abi Talhah reported from Ibn `Abbas: "Do not give them dominance over us, lest we suffer trials by their hands.''
Allah's statement, (and forgive us, Our Lord! Verily, You, only You, are the Almighty, the All-Wise.) means, `cover our mistakes from being exposed to other than You, and forgive us for what (sin) is between us and You.'
(Verily, You, only You, are the Almighty,) `and those who seek refuge in Your majesty are never dealt with unjustly,'
Yusuf Ali Explanation: The men of Faith look forward to Allah. Their quest is Allah, and the object of their hopes is the meeting with Allah. They should strive with might and main to serve Him in this life, for this life is short, and the Term appointed for their probation will soon be over.
The Term (ajal) may signify: (1) the time appointed for death, which ends the probation of this life; (2) the time appointed for this life, so that we can prepare for the Hereafter; the limit will soon expire. In either case the ultimate meaning is the same. We must strive now and not postpone anything for the future. And we must realize and remember that every prayer we make to Allah is heard by Him, and that every unspoken wish or motive of our heart, good or bad, is known to Him, and goes to swell our spiritual account.
Qur'an Wiki: This prayer is an appeal to God not to give the unbelievers mastery over the believers, which would strengthen the former's rejection of true faith.
They would think that had faith provided any protection to its followers, they themselves would not have been able to subdue them. This is a confusing point, one that often surfaces when falsehood manages to gain the upper hand for a time and purpose known only to God. In such periods, tyranny is able to treat believers very badly. Good believers endure this test with patience, but this should not prevent them from praying to God to spare them such hardship that makes of them a test to others and a basis for creeping doubt.
Abraham and his group continue their supplication: "Forgive us." This is said by Abraham, God's own friend, realizing that the standard of worship which is worthy of God is beyond his reach. As a human being, he cannot attain the level of worship which gives due thanks for God's favours and which sufficiently glorifies Him. Therefore, he appeals for forgiveness, setting an example for his own group and all later believers.
Concluding his prayer, Abraham addresses his Lord by His attributes that are the most suitable here: "Lord' You are the Almighty, the Wise." (Verse 5)