Sullivan is adamant that Carroll will now find his form after a difficult first season with the Hammers, as injuries and a lack of form saw him score just two goals in the Premier League following his £15m move to the club.
He told The Mirror: "I still think Andy Carroll will come good. He didn't have a pre-season last year. He never really got his act together because of that and I think you'll see a much better player next season.
"It was a fair decision based on what he did last season. He didn't do enough when he came back.
"And I'm glad he is not playing for England. I don't want him arriving three weeks late because he has been in Rio all summer, particularly on the fringes of the squad not playing or not doing hard training. I'm pleased he wasn't with England this summer. His time will come."
West Ham face Tottenham Hotspur in their Premier League opener on August 16.