The Anfield outfit have been left surprised by his decision to quit after just a season in the position, says Sky Sports.
It comes after owners FSG announced they were exploring new investment opportunities - including the possibility of selling the club.
Carragher, 44, has shed light on the situation, expressing his concern at the "upheaval" going on behind the scenes.
The ex-defender said: "It's not ideal because I think when you're talking about recruiting players, a person in that role is heavily involved.
"Not just for right now, maybe [in] the January transfer window, you're talking about the summer as well.
"So it does feel like a little bit of a shock and I think it is a little bit of a worry for Liverpool right now.
"There seems to be a lot of upheaval behind the scenes in terms of obviously the ownership, Michael Edwards has moved on, Julian Ward came in to replace him and now he's gone as well.
"So I don't think it will be easy to get someone straight away and if it is unexpected for Liverpool and it's come as a shock [then] I'm sure they're not prepared for something like that right now."