Peter points away from himself to Jesus (Acts 3:12-16). What he's emphasizing is this - This is more than what I say about Jesus. It's what the prophets said about Him. This was God speaking through the prophets (Acts 3:18).
"The power of Jesus Christ" (Acts 4:10) - This is more than the healing of one man. This is salvation for all who come to Jesus, the Saviour (Acts 4:12).
"All the people were praising God for what had happened" (Acts 4:21). This wasn't praise for Peter and John. It was praise to God. We must learn to look beyond the servants of God to the God whom they serve.