The Gunners are very much in the title race, just two points behind leaders Manchester United, heading into the final seven matches of the campaign.
Campbell - part of that FA Cup-winning squad at Cardiff in 2005 - believes the current side, led by captain Cesc Fabregas, have the all the talent needed to succeed.
"The lads are playing really well and I am sure with their talent, they can play even better," said the 35-year-old former Gunners skipper, who rejoined the club on a short-term deal during January.
"However, playing fantastic football all the time is great, but ultimately it is about what you can get out of your career.
"Young players have to realise pretty quickly that it is not about one game, but how you perform over the whole season."
Campbell added in the April edition of the official Arsenal magazine: "It is a youthful team and has to learn quickly at this time of the season, because the games come thick and fast - once a game has gone, it is gone.
"If you win, you have to get your feet straight back on the ground and grind out another win.
"You can enjoy the moment, but remain level-headed and always think ahead to the next challenge."
Campbell feels the current squad are starting to get the same vibe as the one which swept all before them with the likes of Patrick Vieira, Dennis Bergkamp and Thierry Henry.
"Every team has its own kind of frequency, and obviously there were different players [when I left] in 2006," the centre-half said.
"Now the lads are young, enthusiastic and blessed with a lot of skill and talent.
"They have a lot of spirit and belief too, like the team before.
"The belief has definitely started to come, and everyone can feel it.
"The manager often talks about belief, but it takes time for it to sink in and for people to really believe."