Derry has named midfielder Luke Berry, 23, as his new full-time skipper after dropping Roberts to the bench for last Saturday's win at Leyton Orient.
"I've spoken to Mark and he's accepted it as a man. He'll respond in the right way because he's a leader of men," Derry told BBC Radio Cambridgeshire.
"But I wanted to appoint Luke because his performances have changed my mind."
Berry has scored eight goals in 33 appearances since returning to the club where he started his professional career in the summer from Barnsley.
Derry continued: "I've always said I'm a massive fan of Luke Berry, I think he's a very good player and can take his leadership qualities into a different area.
"He's never had this tag before. It's a massive responsibility, but when I look around what this football club is, Luke Berry falls in that category and I want him to take this captaincy onto a different level."
Cambridge United defender Mark Roberts has accepted losing the captaincy "as a man", according to boss Shaun Derry.