The pundit thinks his old side will have preferred to exit Europe but beat Manchester City on Sunday, but Everton would swap their results.
The Reds were knocked out of the Europa League on Thursday after being beaten by Besiktas in Istanbul, with the game going to penalties and Dejan Lovren missing the crucial final spot-kick.
Rather than losing confidence though, Brendan Rodgers’ side responded by beating Premier League champions Manchester City at Anfield on Sunday afternoon, putting them firmly into the race for a Champions League place and handing Chelsea a further advantage in the race for the title.
Now, their former defender turned Sky Sports pundit Carragher has said the Reds will likely have preferred to go out of Europe on Thursday given they won on Sunday.
“After the European games midweek for Liverpool & Everton the Blues were celebrating both results, the Reds were doing the same today!” Carragher wrote.
“I think for LFC they'll have preferred to go out of Europe & win today.”
In contrast, Carragher believes that Liverpool’s rivals Everton would have swapped their result on Thursday for a win against Arsenal in Sunday’s other fixture.
The Blues were impressive in their 3-1 win over Swiss side Young Boys in the Europa League, but were then beaten 2-0 by Arsenal at the Emirates on Sunday, leaving them perilously close to the relegation places.
Carragher though, thinks Everton fans would have wanted to win Sunday’s game rather than the tie against Young Boys, but is adamant they’ll be safe anyway.
“I think Everton will be fine & should enjoy their European adventure,” added Carragher.
“[However] I'm sure some Everton fans worrying about getting dragged into a dogfight may have liked a win today rather than going through in Europe.”