Arsene Wenger's side were beaten 3-0 by Everton on Super Sunday, a result that takes Champions League qualification out of their own hands as Roberto Martinez's side are just one point behind them with a game in hand.
Arsenal have spent 128 days on top of the Premier League this season, but Sky Sports expert Carragher now thinks there is a real possibility that they won't finish inside the top four - and he pointed to their slow play as the main reason.
He told Monday Night Football: "We knew the Everton game was always going to be a tough game. You can easily lose there - anyone can - because it's a tough place to go.
"It's the way they lost that's worrying. You watch that Arsenal team now and when I think of an Arsene Wenger team I think of power and pace.
"Watching this team I look at it and think it's weak and slow. That would be worrying. No matter who you play, if you haven't got that pace and strength in your team mentally and physically, even if the fixtures are kind it's going to be difficult for them.
"That's probably one of the slowest Arsenal teams I've seen under Arsene Wenger and that's a massive worry for them.
"With the energy Everton showed in that game I think you would probably have to say they were favourites - but I will change my mind next week!"
Fellow Sky Sports pundit Gary Neville agrees there is a real possibility that Arsenal could fail to qualify for the Champions League for the first time since 1996.
They have reached for Europe's top club competition in each of Arsene Wenger's 16 years in charge and Neville suspects that run will continue because Everton have a trickier run-in with Manchester City still to visit Goodison Park.
However, he says Arsenal's form - the fourth worst in the Premier League in the last six games - suggests they could fall short.
Neville said: "They've never disappointed us in seasons gone by in seeing the job out and recovering. They have shown spirit.
"You just wonder whether this could be one season too far and whether Everton have got such a momentum with them.
"My gut instinct still tells me Arsenal will hang on in there because of their fixtures against Everton's, but I wouldn't be surprised if this was finally the year that Arsenal didn't get into the Champions League space.
"At the moment, the signs are there and it's worrying."