The question of whether Brutus ever does come to the realization that he was wrong to have killed Caesar is never fully addressed in the text of Shakespeare's Julius Caesar. That Brutus realizes the murder of Caesar was a mistake becomes clear in Act IV, scene iii and Act V, scene iv when he sees, and reports seeing, the Ghost of Caesar, but being mistaken can take any number of meanings: a mistaken time, a mistaken group of people; a mistaken method, etc.
Brutus certainly knows when he sees Caesar's Ghost for the first time in his tent, in the latter half of Act IV, scene iii, with the promise that they would meet again at Philippi, that the end of the deed begun on the Ides of March will be his own ultimate defeat and his own death. Earlier in Act IV, scene iii he cautions Cassius that they slew Caesar because he was "supporting robbers," so they must themselves now not become corrupt and take "base bribes." In this Act Brutus is still determined that they acted as honest citizens who wished to stop a corrupt train of bribe takers, countenanced by Caesar, that defiled the Republic.
There are several opinions about the meaning of Caesar's Ghost calling itself Brutus's "evil spirit" ("Thy evil spirit, Brutus"). One logical interpretation is that Caesar is asserting that he will have triumph over Brutus, sort of like the contemporary movie quote, "I'm your worst nightmare," which we all understand to be a direct threat to the hearer.
Here, with the ghostly visitation, is where Brutus must certainly begin to entertain the idea that some error of some sort was made because his only response is to agree that if they must meet again at Philippi, then they will meet again at Philippi. His next response, after the Ghost has faded, is to say that now that he has nerve back, he would converse with the Ghost further. It may have been in this nonexistant conversation that we might have learned more about Brutus's thoughts.
It is in Act V, scene iv after seeing Caesar at the battlefield in Philippi that Brutus bows to the comprehension that he acted wrongly, but it still isn't clear whether he is convinced that is was wrong because his beliefs were mistaken or wrong because Caesar was too powerful to go unavenged or wrong for some other reason: The reason for Brutus's acquiescence to the wrong action is never made clear.
Brutus's last action and last words do make clear that he recognizes that Caesar has avenged himself through the opposing forces:
"O Julius Caesar, thou art mighty yet!
Thy spirit walks abroad and turns our swords
In our own proper entrails." (Act V, scene iii)
It is also clear that Brutus dies in humility with enlightenment of some sort about the mistake he has made in murdering Caesar: "Caesar, now be still:/ I kill'd not thee with half so good a will" (Act v, scene v). But there is no textual evidence to show whether he believes he was philosophically wrong about "supporting robbers;" morally wrong to think that assassination was the right means for removing a corrupt government; intellectually wrong in his definition and assessment of corruption; or personally wrong by being deceived by the other individuals in the assassination plot.