The former Liverpool man believes the Frenchman's desire to be smart in the transfer market sometimes has a negative impact on his quest for silverware.
The Gunners have spent large sums in the last two summer transfer windows in bringing in star names such as Mesut Ozil and Alexis Sanchez, but before then have spent more frugally.
The money has always been available at the Emirates, but manager Wenger has often preferred to develop talent rather than spend large sums on established players.
And Carragher believes that is what may be holding back the side in their quest for silverware.
“The thing with Arsene Wenger is I feel he always wants value in the market, and he always wants to wait, he's patient,” he said.
"He spends the money like it’s his own, that's the way he runs the club, you can admire that in some sense. Rather than what [Jose] Mourinho did, he got Costa he got Fabregas. But I think maybe that sometimes holds them back."
The former Liverpool defender does, however, believe that the Gunners could be genuine title challengers alongside Manchester City and Chelsea next season.
Wenger’s side are currently third in the table, level on points with City in second but with a game in hand, having enjoyed an impressive 2015 in which they have won 18 of their 22 matches.
It is that form which has convinced Carragher that they could be genuine contenders next season, while he also believes there may be a gap opening up over the likes of Manchester United and Liverpool as well.
"I think they've joined those top two sides that we think every season are going to go for the title. They're so close,” he said.
"What we've seen of Arsenal of late is that they are with the three best teams now, and then there's a little level to Manchester United and Liverpool just behind.”