West Ham splashed a club record 15 million pounds ($24.42 million) to sign the burly target man from Liverpool on a permanent deal in June after he spent the previous season on loan at Upton Park.
He has yet to make an appearance since completing the move, however, and is still at least three weeks away from fitness as he recovers from a fractured foot.
"Had we known he would be out for this long, we would not have signed him," Sullivan told the BBC's Football Focus.
"We are not a rich enough club to deal with that. You know any player can get injured but we can't buy a player knowing he is going to be out for half the season.
"When we signed him we were assured by the medical staff that the very, very latest he would be back was Sept. 1. That would have meant he would only miss two league games."
Carroll, an England international when fit and on form, became Britain's most expensive player in January 2011 when Liverpool signed him from Newcastle for 35 million pounds on transfer deadline day.
Then Liverpool manager Kenny Dalglish struggled to coax Carroll's best form from the towering forward, whose time at Anfield was also punctuated with injuries.
The 24-year-old was loaned to West Ham in August 2012 as Liverpool changed their playing style under manager Brendan Rodgers, with quick passing and possession preferred to the more direct approach that Carroll thrived on.
West Ham saw Carroll as a marquee signing and a significant step as they prepare to move to the 54,000-seater Olympic Stadium in 2016.
It has proved an unsuccessful gamble so far and in Carroll's absence the club have been drawn towards a relegation battle.
"Even now we haven't got a date that he could be back. He could be back in three weeks, he could be back in six or eight weeks. I hope he might make a contribution in the next three or four weeks, that might be 20 minutes as a sub," Sullivan added.
"He is not going to be quite the player he was at the end of last season until he has played some games.
"He is a fantastic player, don't get me wrong, but I only wouldn't have signed him because I can't have that amount of wages and that amount of transfer fee on a player who isn't going to play a minimum 20 or 30 games a season, hopefully 38 games a season."
West Ham host bottom club Sunderland on Saturday (1500 GMT). ($1 = 0.6143 British pounds)