In response to their lack of understanding, Peter preaches to them. "Did you think that we did this? Have you forgotten the God of Israel? You may have rejected Jesus, the one that God chose, but God has not rejected him."
We today are living among people who also have heard about God, about God's gifts, and God's faithfulness. Yet, they don't expect God to do anything good for them, and they don't recognize when God does. They may have neglected God or they may have collaborated in acts that were in opposition to what God wished.
Peter preaches, "Repent. Even your sins can be forgiven.
Tangent: Verse 16 says that Peter was able to heal the man through faith, but is not explicit whether Peter is talking about his own faith. Nothing is said about the beggar's faith before the healing (1-10).