Carroll has struggled with injury problems this season and has not played regularly. When the 27-year-old striker has played, his performances have not been great.
Sullivan, though, believes that the England international will get back his rhythm in due time.
The West Ham co-chairman has also stated that he hopes that the former Newcastle United striker makes a positive impact against Liverpool and Norwich City this week.
“On a positive note it was great to see Andy Carroll back out on the pitch,” Sullivan wrote on West Ham’s official website. “It might take him a few games to get back to his best, but I hope he he has a real impact against Liverpool and Norwich this week.”
Carroll has scored three goals and created five chances in 14 Premier League appearances so far this season.
The former Liverpool striker has a pass accuracy of 63% and a shot accuracy of 61%, and has won 45 headers, three dribbles and one tackle.
West Ham will host Liverpool at the Boleyn Ground in the FA Cup fourth-round replay on Tuesday evening.
Then this coming Saturday, Slaven Bilic’s side will face relegation candidates Norwich City away from home at Carrow Road in the Premier League.