The Gunners have failed to lift the top-flight title since the 2003-04 season and haven't won a trophy since their FA Cup triumph in 2005.
Adams told The Sun: "It's time that Arsenal won something again, even the FA Cup or League Cup. But I can't see it, to be honest.
"They are still not good enough in certain areas of the team. And they are miles off the title."
Adams played over 650 games for Arsenal during his 18-year career with the club.