Liverpool were in line to win their first ever Premier League title but were pipped to the crown by Manchester City.
The Reds finished one point behind Pep Guardiola’s side on 97 points despite losing just once all campaign.
Klopp improved Liverpool’s strength in depth last summer, bringing in the likes of Xherdan Shaqiri, Naby Keita and Alisson.
But Carragher believes better back-up choices are still needed in two key areas of the pitch.
“I think we could do with a defender, a full-back who can play both right-back and left-back,” Carragher told the Liverpool Echo.
“I don’t think the cover for Trent or Robbo has been at the level we have needed at times.
“We’ve had to use James Milner and Jordan Henderson there and they do really good jobs, but it’s not like having a proper full-back there.
“We need another attacker on the level of the front three. Not a centre forward. People are saying we need a striker, but I don’t believe that.
“Another Mane type, maybe a bit younger and up and coming. People talk about the Ajax wide players, I don’t know too much about them other than seeing them in the Champions League.
“But somebody who can play left, right and through the middle, who can move about.
“So you’d have four players going for three positions. And you’d still have Rhian Brewster coming through and Divock Origi.
“We don’t need a striker because Mane and Salah can play up front, and Firmino is first choice.”
Klopp himself wants to work with and develop his current crop of Liverpool players having splashed around £170million last summer.
He recently said: “For sure there’s no need for that level (of spending).
“I don’t want to talk exactly what we will do, but I don’t think this is a team at the moment where we have to spend the big money or whatever.
“The best way to do it is bring together a group of players, try to develop them altogether and then stay together for a while.
“That was maybe the main problem of Liverpool for the last decade.
“When they had a good team after a season they went all over the world. That will not happen this year for sure.”