γνωστὸν οὖν ἔστω ὑμῖν, ἄνδρες ἀδελφοί, ὅτι διὰ τούτου ὑμῖν ἄφεσις ἁμαρτιῶν καταγγέλλεται [καὶ] ἀπὸ πάντων ὧν οὐκ ἠδυνήθητε ἐν νόμῳ Μωϋσέως δικαιωθῆναι, ἐν τούτῳ πᾶς ὁ πιστεύων δικαιοῦται.I have neither the time nor the expertise (in NT studies or the debates about justification) to enter into a full treatment of this passage, but I did want to offer a thought. I have looked at a few commentaries (Fitzmyer, L.T. Johnson, Bock), none of which related this statement at all to the preceding emphasis on the resurrection.
But it seems to me that the context of the sermon, the context of Acts as a whole (which emphasizes the resurrection quite a lot--see 2:24-35; 4:2; 17:32; 23:6; 25:23, just to name some references off the top of my head), and the situation in which the sermon was delivered, in a synagogue among Jews who knew that Leviticus promised forgiveness of sins through sacrifices--all of this indicates that while Paul here certainly related this 'justification' to forgiveness of sins, perhaps more specifically he relates it to forgiveness of sins that liberates from the curse of sin = death.
To be brief and simplistic, in his letters Paul speaks of Adam's sin as ushering in death (Rom. 5:12-14; 1Cor. 15:21-22), so that death is the consequence of sin. Now, Paul in Acts could be saying to the Jews in Antioch: "The Torah promised forgiveness of sins through slaughtering a goat, but it never promised justification that you would not suffer the effects of sin, that is, death. No matter how many goats you slaughter, you will die. The Torah cannot set you free from death. But Jesus can. What the Torah could not justify you from (= the effects of sin = death), Jesus does justify you from. He has inaugurated the resurrection, he did not see corruption, and everyone who believes can join him in that."