The Gunners clinched fourth place ahead of neighbours Tottenham on the last day of the Premier League season to secure Champions League football for next term but, after another trophyless season, calls for investment are growing.
Adams, who captained the Gunners to 10 major trophies during his 22 years at the club, believes that manager Arsene Wenger must invest in the squad, prioritising the defence.
|8/11||Arsenal are 8/11 with BetVictor to finish in the Premier League top four in 2013-14
The former England captain also urged fans to be patient with the young team, with the hurdle of winning their first trophy the most crucial to overcome.
"The fans are desperate for a trophy of some sort," Adams added. "I would like the players to get used to winning; if you have never had that experience of crossing the line as a winner you don't know what it is like to be a winner.
"Jack Wilshere is very important to the club but you can't rush him. I think he has played more games than Arsene would have wanted him to play following his injury but he's such an influential player for us."
Likewise, former 'Invincible' Pires believes that Arsenal need to heavily invest in the squad this summer but, importantly, they must retain their long-serving manager.
"Wenger built Arsenal so he is very important to the players and needs to stay," the Frenchman observed.
"In my opinion I think Arsenal need to buy English players. Wenger has changed the philosophy at the club, he brought in young players like Theo Walcott, Alex Oxlade-Chamberlain and Aaron Ramsey; these players are very good for the future but now they need to buy some players with experience to give a good mix."