The Gunners failed to claim a Champions League spot in the 2016-17 campaign for the first time in two decades.
During Sky Sports' Monday Night Football, Carragher said: "I have always questioned Arsenal's mentality, but I have always thought they are good enough. I still question their mentality, but they are not good enough now, and that's the big thing.
"Arsenal are actually getting worse. They're not getting better. If you go back to the Monday Night Football we did, I think against Crystal Palace, at the back end of last season, I called them cowards.
"Afterwards, when you calm down a little bit and reflect, maybe you think that was a bit strong. Them stats back me up. 21 points from 26 away games is an embarrassment for a team that is supposed to be one of the top teams in the country."