The north London club finished second in the 2015/2016 Premier League, 10 points behind champions Leicester City.
It has now been 12 years since they last won the league, but Djourou has suggested that run will soon end.
“They haven’t won it for a long time. That hurts them. It hurts the club, the fans, the players of course. It’s not like they don’t want to win,” the Switzerland international told the Daily Mail.
“It’s important people know that. Every time they don’t win they are criticised for not winning more than any other club.
“But there are a lot of positive things, they are just missing some little pieces to the puzzle. I’m sure they will get it right.”
There is a fear that Arsenal could fall behind the pack next term, after Pep Guardiola and Jose Mourinho’s arrivals at Manchester City and United respectively.
However, Djourou said Arsenal’s fans should not forget everything Wenger has achieved during his two decades in charge.
“We’re in a game now where it’s changed – people expect more. They are frustrated.
“I can understand that, but they shouldn’t forget what Arsène has done for this club. We can forget so quickly.”
The 29-year-old, who is now at Hamburg, spent 10 years at Arsenal before moving to the Bundesliga in 2014 after an initial loan move.
Having already added Granit Xhaka to their ranks, it has been widely reported that the Gunners are close to signing Leicester striker Jamie Vardy, who was involved in more goals (30) than any other Premier League player this season.
Alongside Xhaka, Djourou is part of the Switzerland squad who will begin their Euro 2016 campaign on 11th June against Albania.