The Spaniard collected a 2005 FA Cup winner's medal with the Gunners, albeit as an unused substitute, but that remains the north London side's last major trophy.
The likes of Thierry Henry, Samir Nasri, Cesc Fabregas and Emmanuel Adebayor have since departed for significant fees and the club's apparent reluctance to invest in proven replacements has deepened the frustrations of fans who have seen their team trail the likes of Manchester United, Manchester City and Chelsea in the battle for silverware.
Almunia told The Sunday Mirror: "As a player at Arsenal, it is hard to see the best players go to other clubs every year. They have missed a lot of great players in the last few years.
"The first year I came to England, I thought 'Oh, I'm going to win a lot of things with Arsenal' but the change then started. The club has been changing every year."
There remains a danger of Robin van Persie, named Professional Footballers' Association and Football Writers' Association player of the year after scoring 37 goals in all competitions last season, leaving the Emirates Stadium this summer.
But the arrivals of Lukas Podolski and Olivier Giroud have encouraged Almunia, now with Watford, to believe this could finally be Arsenal's year.
His compatriot, Malaga midfielder Santi Cazorla, is also expected to sign in the coming days while Arsene Wenger has been heavily linked with a move for Real Madrid's Nuri Sahin.
"One of these years, everything has to come together and be perfect, and now is the time for Arsenal," Almunia continued.
"They've signed some good players this year, Santi Cazorla is fantastic."