The north London side were beaten 2-1 by Watford at Emirates Stadium in the quarter-finals as they failed in their attempt to win the competition for the third year running.
Arsenal now turn their attentions towards their Champions League showdown with Barcelona on Wednesday night, as they look to overturn a 2-0 first-leg deficit and book their place in the quarter-finals.
The Gunners have been struggling to find consistent form in recent weeks and have only won one of their last seven games in all competitions.
And former Liverpool defender Carragher admits that he feels Arsenal could struggle to claw themselves back into the title race.
Carragher told Sky Sports: “I think it will be difficult for them now.
“Psychologically these defeats and going out of the Cup and Champions League – they’re out of that, forget the second leg – and then to lift themselves with the form they’re in.
“[Wenger] keeps talking about the spirit in the squad, but it’s more in hope and belief that it will come to the fore. The next home game is Watford and they’ve got two difficult away games in Everton and West Ham.”
Arsenal are currently third in the Premier League table and eight points behind leaders Leicester City.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news