Adams spent just under 20 years representing the Gunners, collecting four league titles and three FA Cups during a glittering career that saw him captain Arsene Wenger's side to the double. In recent seasons Arsenal fans have had to endure seeing their most prized assets sold to other clubs, with a high number remaining in England and representing major rivals.
The likes of Emmanuel Adebayor, Samir Nasri, Robin van Persie and Cesc Fabregas have all been allowed to leave the Emirates, with only the latter moving abroad, and Adams said: "The game and society have both changed in that respect. When a foreign player comes over to play here it is natural maybe that he goes back."
He added: "Cesc, it was a natural progression to go back because he thought Barcelona are bigger than Arsenal.
"I don't know what he is talking about because I'm an Englishman who wouldn't even go to Manchester.
"What would I go to Manchester for? Arsenal are massive to me and that proves there is a different mentality in the people that are now playing in the top league in the world."
Former England international Adamson Sunday offered his services to Arsenal to assist in any way they deem fit, whether it is sitting on the board and making the tea.
The 46-year-old has also backed the board to properly fund Wenger in the transfer market this summer but admits he would rather see a large fee splashed on a marquee signing rather than bringing in a number of targets.
"In the last few years we have let our better players go and they need replacing," he added. "What I hope they are doing is not gambling so much on three or four players but bring one player in who is going to make the difference. I don't think we have time for a 'maybe' player to come through."
Real Madrid forward Gonzalo Higuain is believed to be on the verge of a move to Arsenal, whilst there remains a strong link to a bid for Manchester United's Wayne Rooney.