He also said their policy of letting their best players leave was wrong and is costing the club dearly.
Adams was speaking to BBC Radio Five Live following their 2-1 defeat at Manchester United on Saturday which left them in sixth place nine points behind top-placed United in the title race.
Arsenal have finished in the top four for the last 16 seasons but Adams, who made nearly 700 appearances for Arsenal between 1984 and 2002 was highly critical of his old club.
"You need to keep your best players and in recent years we've let them go a bit easy," Adams, 46, said.
What pained Arsenal fans most on Saturday, despite their team's poor performance, was that United's opening goal came from Robin Van Persie, who scored 37 goals for Arsenal last season, but was allowed to move to United for in the close season.
In the last two years Arsenal have let Van Persie, Alex Song, Cesc Fabregas, Samir Nasri and Gael Clichy all leave as their contracts wound down.
"I never got anywhere near the last year of my contract," said Adams.
"You don't let them go into their last year and run their contract down. It's about winning, and how do you win? You have the best players, and if you keep selling your best players you're not going to win.
"There's been so many players who have moved on and are doing great jobs for other teams, the list is endless."
Adams added: "If Wenger gets them in to the top four this season, he would have done brilliantly."
Arsenal fans meanwhile took to social media sites to pillory their defender Andre Santos who asked for Van Persie's shirt as a souvenir as the two walked towards the tunnel together at half-time.
Santos had a poor match and was criticised by many fans who claimed he should be disciplined for asking for the shirt with the match still in progress.
The Sunday Telegraph commented: "Having produced a woeful individual performance in the first half, the Brazilian defender appeared more like a star-struck groupie than a committed opponent as he took the Dutchman's shirt."
As well as now facing an uphill fight to win the Premier League title for the first time since 2004, Arsenal travel to Germany this week fighting to keep their Champions League prospects alive at Schalke 04 after their 2-0 home defeat to the Germans two weeks ago.
