Carragher, speaking on the Sky Sports Football Podcast, said it was likely the management style and demeanour of Rafa Benitez which saw the Reds go for the Madrid-born boss at the time.
The 42-year-old said: "Gerard Houllier had lost his job, and (chief executive) Rick Parry had interviewed Rafa Benitez at some stage.
"He was just keeping the senior players informed about where they were up to, and he did mention Jose Mourinho.
"I knew much more about Rafa Benitez because of the Spanish football and what he'd done, and it looked that (appointing him) was quite far down the road anyway.
He continued: "I think even that run down the line, even though it was great, at Old Trafford, the feeling was at the club and maybe from certain players that it wasn't really the Liverpool way of doing things.
"So I always thought we'd go for Rafa with him being a little bit more standoffish."