Berbatov joined the Cottagers on deadline day from Manchester United.
Allardyce told Sky Sports: "We couldn't afford him. The problem was the transfer fee and the size of the salary was out of our domain this season in terms of our budget. Fulham created their own transfer funds. They knew Clint Dempsey was moving on, and one or two others, and that gave them the opportunity to go big.
"They were interested in Andy Carroll as well, I believe, and we were glad to get Andy on a loan basis but they obviously clinched Dimitar Berbatov. I think he was on his way to Italy, but it shows you how popular the Barclays Premier League is that he turned down a move to Fiorentina because he wanted to move down to London and play for Fulham."