The newly promoted Premier League club had wanted to hold onto both Stuart Armstrong and Che Adams.
However, the duo have departed as free agents, while goalkeeper Alex McCarthy has stuck around.
"I always believe in my ability, anyway. I'm the sort of person that will always go out and train properly," McCarthy told the Daily Echo.
"I'm always trying to improve so it was never a worry for me, sort of, coming into the team. I'm always backing my ability and I know what I can do.
"To come into the team at that late stage in the season and help the club get back to where it should be was a good start to the summer for me.
"My contract was up at the end of last season and, to be honest, I hadn't really thought about what I was going to do next.
"I just wanted to come into the team and do the best I could to help the club get back to where it should be."