The Manchester United boss feels that the Reds rushed into purchasing the England striker for £35 million and believes they expected to sign Clint Dempsey before loaning him out
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The Old Trafford boss believes that Liverpool should have done a bit more research on the former Newcastle player before deciding to shell out such a sum for a relatively experienced player at Premier League level.
Carroll struggled to hold down a regular starting place after arriving on Merseyside and joined West Ham on loan in the summer.
"He'd played not a lot of games for Newcastle and had to deal with a £35m transfer to a club like Liverpool," Sir Alex told the Sunday Mirror.
"He was young and it was quite a big jump for him for that kind of money. We've gambled on a couple of players in the past, a couple of million, something like that.
"But when you get to that level of £35m, you need to a bit more homework and see how he is in the second season, maybe."
The 70-year-old hinted that Brendan Rodgers' inexperience might have been a factor when he allowed Carroll to leave for Upton Park before completing a deal to sign Clint Dempsey, who eventually joined Tottenham.
"They were after Clint Dempsey, that didn't work out, and they had done the deal for Carroll," he continued.
"Maybe it was something they did not expect. With the manager being young, maybe he expected the deal to go through and it was not there and he had lost a player, too."
Sir Alex did expect Carroll to pose a threat when United host West Ham in the Premier League on Wednesday evening.
"Now it's up to the boy to improve himself," he concluded. "He's a great header of the ball and very aggressive. He'll be a handful on Wednesday."