The Gunners have lost a handful of stars over the last few years, with the fans having to adjust to life in wake of departures of the likes of Samir Nasri, Emmanuel Adebayor, Cesc Fabregas, Robin van Persie and Bacary Sagna.
Vermaelen became the latest star to leave when the Belgium international centre-back agreed to join the La Liga giants over the weekend.
The defender left the Emirates Stadium for around £15 million and Adams, who played for the club for 19 years from 1983-2002, believes that all too often the North London outfit are moving on their big-name players.
He also stated his belief that the Londoners would be "struggling" to finish in the top four this season without the services of the 28-year-old, let alone challenge for the Premier League title.
Speaking to BBC Radio 5Live, Adams said: “I’m slightly saddened by the news Vermaelen’s leaving. I personally believe that you need three central defenders to win the championship.
“It seems kind of too easy to say, ‘I’m not playing – off I go’. It seems like it’s far too easy to let these people walk out the door.
“Defensively, I think it’s going to be a huge loss. I put them down as third before Thomas went. Thomas goes, you’re struggling to get in the top four."
Adams also said that there was "no more excuses" for manager Arsene Wenger, and claimed that their strong financial footing puts them in an ideal position to compete for the league.
The last 12 months has seen Wenger land Alexis Sanchez and Mesut Ozil for a combined fee of around £75m, while the Frenchman has also brought Mathieu Deubchy, Calum Chambers and David Ospina to the club this summer.
However, he believes that the Gunners' current crop do not have the right mentality to grind out the type of results that lead to finishing top of the pile after 38 games.
“There are no more excuses, for me," he added. "The finance is there, everything’s in place. Don’t let your players go. Challenge for the title.
“I don’t think there are those characters in midfield and defence that could go away from home and keep clean sheets, at Manchester City, Chelsea and Liverpool – grind out a 0-0. For me, the team that wins the league does that.
“In the past, there were financial problems with the building of the new stadium. But the business model’s fantastic. Year in, year out, they’re making profit now.
“And if they want to compete against Real Madrid or Barcelona or Bayern Munich now, and Man Uniteds and Chelseas, you’ve got to keep hold of your better players."
Arsenal begin their new campaign with a visit from Crystal Palace on Saturday evening, fresh from their 3-0 win over Manchester City in the Community Shield on Sunday.