Liverpool attacker Nunez has had an inconsistent spell at the Merseyside club.
In his two season at Anfield, he has often stunned the fans with his brilliance, or stunned them with his shortcomings.
Everton, the opposing team from Merseyside, may have ruined the Reds' chances of winning the Premier League during Jurgen Klopp's farewell campaign after a 2-0 defeat at Goodison Park.
In either half, Jarrad Branthwaite and Dominic Calvert-Lewin scored to ensure the win for the Toffees.
Carragher singled out Liverpool striker for his performance against Everton with a brutal assessment.
"The chance that Nunez misses before half-time, that is unforgivable at this level," said the Liverpool legend, as quoted by Liverpool Echo.
"That is not acceptable at this level, certainly when Liverpool are going for the title."
The football pundit believes Liverpool have a big decision to make over the future of Nunez this summer.
In 92 games for the club, the former Benfica striker has scored 33 goals. His inconsistency at the top level has drawn criticism from fans and pundits on a regular basis.
Liverpool attacker Mo Salah and Darwin Nunez failed to make an impact against Everton.
"I think there is a question to ask," he added.
"You want him to do well because there is so much that you like because he gives everything, he runs and causes trouble and gets the odd goal and gets an assist.
"You are looking at it now and after two years, I don't think there is going to be a massive improvement in him. What we have seen in the last two years is what he is.
"He can cause trouble, he can be erratic with his finishing. I don't think it is going to be enough to win you the biggest trophies so I think there is a big decision to be made on him in the summer."
Liverpool are possibly out of the title race
The result against Everton comes as a huge blow for the Reds, who are now three points behind Arsenal in the title race.
Klopp's men are one point ahead of Pep Guardiola's Manchester City, but the Sky Blues have two games in hand over their title rivals.
The performance and the defeat looked like the final nail in the coffin for Liverpool's title race.
It continued the recent bad results for the club, after defeats against Crystal Palace and Atalanta at Anfield.
Just a month ago, the Reds were fighting for a quadruple in Klopp's last season. However, it looks like they are going to finish the season with just the Carabao Cup.
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