It comes after the former defender claimed Mohamed Salah was not the player Liverpool boss Jurgen Klopp wanted to sign when the winger arrived on Merseyside in 2017.
Carragher revealed that Klopp wanted to sign Borussia Dortmund star Julian Brandt, then of Bayer Leverkusen.
Salah has since gone on to become one of the greatest players of the Premier League era having netted 204 goals in 332 games for the Reds.
Carragher claims the club's decision to go for Salah shows why managers should not always have the final say on transfers.
"When he initially came in, an interesting one was Mohamed Salah and Jurgen Klopp is open about this," Carragher said on the Stick to Football podcast.
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"He didn't want to sign him, he wanted Julian Brandt. Liverpool had tried to sign Salah before he went to Chelsea and the people behind the scenes at Liverpool were still there and Salah then went to Roma, and they were very adamant that they had to sign this player.
"You look at what Mohamed Salah has done, but it could have easily gone the other way.
"I do feel that this idea that managers should buy every player isn't right, but a manager shouldn't have a player pushed on him.
"I don't think a manager should just be able to do what he wants, you look at Manchester United and it's worrying, it feels as if he's [Erik ten Hag] just bought every player he knows."
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Salah, who is away on Africa Cup of Nations duty with Egypt, has been a key component in the Reds' surge to the Premier League summit this season.
Meanwhile, Brandt has forged a good career at Dortmund, scoring 37 goals in 193 games for the Bundesliga giants.
But few would argue that between the two stars, Liverpool made the right choice at the right time in splashing £34million on the Egyptian.