The Reds slipped to a 13th defeat of the season on Tuesday evening as they were narrowly beaten by Turkish giants Galatasaray in the Champions League.
Slot had won 62 out of his 99 games in charge of Liverpool before the clash and fans are growing frustrated with the Dutchman whose inconsistent performances are hurting the club’s trophy chances.
Speaking after the clash, Carragher says replacing him won’t significantly change the side who need more squad depth.
"And it's not just a defeat, I think the performances from Liverpool this season are a big worry for the manager. I think I said on this show in the group stage he's got to do something, he's got to change something.
"He's tried everything really, in lots of different ways, but nothing seems to be able to work and it's just at no stage this season have I ever felt Liverpool were in control of a football match. It's either end-to-end basketball, so he wanted to stop that and change that, and then it becomes slow and boring and predictable.
"Do I think another manager could come in straight away, or any manager, say you give him that squad? I don't think it dramatically changes. I really do think the makeup of the squad, how it's been put together, the lack of options in certain areas, is a big problem as well. So it's not just all about the manager but as we know, managers carry the can."
It is all to play for in the second leg at Anfield next week as Liverpool aim to turn the result around in front of the home fans. First, The Reds must face relegation candidates Tottenham in what is a must win for Slot if he wants to secure Champions League football.