The Gunners suffered their first defeat of the campaign on Monday evening as they were beaten 3-1 by Liverpool at Anfield.
Arsenal took the lead through Alexandre Lacazette but Liverpool dominated for the majority of the match and goals from Sadio Mane, Andy Robertson and Diogo Jota sealed the win for the Premier League champions.
But despite their latest setback, Carragher believes Arsenal are on the right track under Mikel Arteta.
And the former Liverpool defender feels the Spaniard is the best man to get the Gunners back into the Champions League.
‘I think it’s almost an identical job to what [Jurgen] Klopp came into. Klopp came into a Liverpool squad where they weren’t even qualifying for the Champions League. That’s what Arsenal haven’t done for the last few years.
‘The first thing for Arsenal is to get back into the Champions League. I think there’s a good chance they can. I didn’t believe that before the start of the season.
‘I like a lot of what Mikel Arteta is doing. I don’t think it’s possible for him to get any more out of the group of players he’s got.
‘Do I think Arsenal could win a title in four or five years? It’s still very difficult and probably shows what a good job Jurgen Klopp has done.
‘But Arsenal have got a really good manager.’