English Standard Version (ESV)
I have always admired Peter's courage. Here, in front of a crowd of people, he accuses them directly of killing Jesus, the Author of life, whom God raised from the dead. He pulls no punches and directly implicates them in the death of the long-awaited Messiah. He doesn't soften his words so as not to offend. He isn't concerned about their feelings -- he is worried about where they stand in relation to God.
The people here are accused of two things -- the first is that they have lost the ability to be amazed at what God is doing. Peter hints toward the amazing miracles God has done in the past, and that we shouldn't ever be surprised when God does a miracle -- human history is littered with miracles God has done, and it's important for us to remember that God has done amazing things out of love for his people.
The second thing they did is that they sinned against God by rejecting Jesus. We often forget that our sins are sins against God -- that in choosing other things to worship, we reject God and choose our own interests. We don't just sin against our fellow humans, we sin against God, and for this reason we are in need of a Savior, whom God graciously sends in Jesus Christ.