Arsenal are one of the favourites to win the UEFA Champions League after dispatching of Bayer Leverkusen to set up a quarter-final clash against Sporting.
The Gunners are on the hunt for a historic quadruple, and are rated by many as strong candidates to sweep all four trophies.
While praising Arsenal's ability to "grind teams down" and "get over the line" in matches, Deeney believes their lack of that winning aura in big European ties could prove costly against elite continental sides.
“If you ask me right here, right now, do I think Arsenal win the Champions League? I would say no,” Deeney stated.
He elaborated: “I think they can do more and can be fantastic but do I think they beat PSG? No. Do I think in a two-legged game they beat Bayern Munich? No. I know they beat them in the group stage but over two legs?
“The point I’m making is when you watch Arsenal they don’t give you a sense they’re going to win the Champions League but you do expect them to get the job done so it’s a weird feeling.”
The Gunners will now turn their focus to the Carabao Cup final against Manchester City this weekend.
Arteta's men will be looking to deliver a psychological blow to their closest challengers by winning the first trophy of the season at Wembley.