Saturday's 2-1 win was the Blues' fourth cup final victory in six seasons, a period of dominance not witnessed since the competition's infancy in the late 19th century.
Terry became the first man to captain the same club to four FA Cup wins - his fifth success overall - while caretaker manager Roberto Di Matteo became the first to both score for and manage the same club to victory in the competition.
The cup has been devalued in recent seasons by the number of Barclays Premier League teams who do not take it as seriously as they once did.
Terry insisted there was "no chance" of that happening at Chelsea while he and Di Matteo remained at Stamford Bridge.
"Growing up, it was what I lived for, even in front of the league," he said.
"Maybe that's changed a bit but, when I was younger, the FA Cup was the biggest competition in world football.
"We've got a good base of appreciation of the cup and the foreign players when they arrive soon know what it means to this club."
No-one more so than Didier Drogba, who became the first man to score in four cup finals, or Petr Cech, whose wonder-save from Andy Carroll landed him a fourth winners' medal, equalling the record for a goalkeeper.
Drogba appears certain to quit Stamford Bridge when his contract expires this summer.
Terry said: "It will be such a shame because he's been incredible for this club.
"Throughout the world, when people look at Chelsea, they think of Didier and Lamps (Frank Lampard) and these kind of players. They are Chelsea.
"Did loves the club. We've got a massive Champions League game in a couple of weeks and, after that, hopefully something can be thrashed out and he stays."
He added of Cech: "I think we've got the best keeper there is.
"You look at Didier for his goals and his memories on the Wembley turf - the big players step up on the big occasions and Didi and Big Pete did that."
Terry and Drogba's records may never be broken and surely no-one will match the seven FA Cup triumphs of left-back Ashley Cole.
Terry said: "Seven times, it's flipping well beyond anyone else.
"He had some great times at Arsenal and even better here.
"Winning trophies like this is what it's all about.
"This is what you hope for in pre-season, to be involved in competitions right at the end. And we are."
With the Champions League final to come, there will be little time for Chelsea to celebrate yesterday's win.
But Terry said while clutching a bottle of beer: "Moments like this don't come along often and it's important to spend it together as a squad and enjoy the good times.
"There's no party planned because of the Champions League and everything.
"The club normally put on something but I'm sure the players will come up with a few ideas."