The 25-year-old centre-back was a villain for the Reds as they crashed out of the European competition.
Having won the first leg of the round-of-32 tie against Besiktas 1-0 at Anfield last week, the Premier League outfit were expected to progress to the last 16.
However, Liverpool lost the second leg 1-0 in Istanbul on Thursday, which saw the tie go into extra time and penalties.
The Premier League outfit lost the penalty shootout 5-4, with summer signing Lovren missing the crucial spot kick.
The Croatia international is having a torrid debut season for Liverpool and has come under criticism from the fans for his failure in the shootout against Besiktas.
Former Liverpool defender Carragher, though, seems to have some sympathy for the ex-Southampton star, and hopes that he recovers quickly from Thursday’s disappointment.
@DejanLovrenLFC6 That was quick! Don't worry head up big game Sunday!!— Jamie Carragher (@Carra23) February 26, 2015
Liverpool were hoping to win the Europa League this season, and getting knockout out at the round-of-32 stage will certainly come as a blow to manager Brendan Rodgers and his players.
However, the Merseyside outfit will have to recover quickly, as they face defending English champions Manchester City at Anfield in the Premier League on Sunday.
Liverpool are in great form in the league at the moment and will be confident of picking up all three points against the Citizens.
The Reds are currently sixth in the Premier League table with 45 points from 26 matches, just two points behind fourth-placed Manchester United.