Carragher was on Sky Sports as part of the punditry group for the Merseyside Derby on Wednesday, which Everton won 2-0.
"The chance that (Darwin) Nunez misses before half-time, that is unforgivable at this level," said the ex-Liverpool captain.
"That is not acceptable at this level, certainly when Liverpool are going for the title."
"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.
"But after two years when Liverpool this season are going to the title and those big games, you need your man to score away at Old Trafford, away at Goodison, in the European game at Atalanta. There is no time to waste, this is not October or November. This is the business end
"In terms of Nunez and where the club go forward now, we have all been in squads where someone comes in and maybe you talk about the first year and maybe say, okay he's getting up to speed with and he's improving, and it looked like he was at the start of the season. But it has ground to a halt.
"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."