Contract rebel Theo Walcott could become the latest name to leave the club after failing to agree a new deal at the Emirates.
Adams told talkSPORT: “I never got into the last year of my contract when I was at the club. David Dein, and the people who were running the club, always made sure I had two or three years to run [on my deal].
“They shouldn’t have sold Robin van Persie because you need to keep hold of your best players. They made a mistake there, they should have wrapped Robin's contract up earlier.
"It’s not about finance, they are going to miss Robin’s goals. If you then drop out of the top four then the money [they would have spent on van Persie] would have paid for itself.
“I can see the fans are frustrated, however I do agree with Arsenal’s principles. No one player is bigger than the club.