The Reds ended a run of three consecutive defeats by beating RB Leipzig 2-0 in Budapest on Tuesday.
More crucially, though, the result gave Jurgen Klopp’s men a firm advantage in their last 16 Champions League tie.
However, speaking to CBS Sports, Carragher outlined why he is not willing to go overboard with a sense of relief.
Indeed, he pointed out performances such as the one against Leicester last Saturday and against Manchester City as games in which Liverpool have played a similar way.
“I saw a Liverpool performance that I have seen in the last few weeks,” the pundit said. “Liverpool’s energy, the pressing has been there for a few weeks and it was there from the start.
“I am not trying to take anything away from that result. That’s a magnificent result. That team is just behind Bayern Munich in the Bundesliga and they did really well in the Champions League last season.
“But they haven’t created an awful lot. Then one mistake, the ball has gone into the opposition net, and they got away with it because of the goalkeeper at 0-0.
“For how well Liverpool played tonight, they still didn’t create an awful lot tonight themselves. For me, going forward that’s still a problem.
“But the actual goals scored were on the back of mistakes and they were clinical. They still didn’t create an awful lot in the game. Again, I am not being critical.”
Goals from Mohamed Salah and Sadio Mane earned Liverpool a significant advantage ahead of the second leg at Anfield, and the online betting odds will be one to keep an eye on ahead of the second match.
Klopp urged to raid Wolves
Meanwhile, Liverpool have been encouraged to make two signings perfect for Jurgen Klopp’s style of play by former Reds striker Emile Heskey.
The reigning Premier League champions bolstered their defensive ranks by bringing in Ben Davies and Ozan Kabak on deadline day.
However, their attack has often misfired this season, with back-ups Divock Origi and Xherdan Shaqiri struggling to make a mark when standing in for Salah, Mane and Roberto Firmino.