Steve appreciated each of his friends. Because he was the boy who's only friend was Bucky Barnes. So after the serum, he took to Peggy and Howard, the Howling Commandos. Then the Avengers and eventually, Sam. He held onto them. When Peggy died, he felt like he somehow failed her, despite her dying of natural causes.
"I'll be your friend. I figure after what we've already been through in the past 24 hours, that was a given."