Terry and Lampard each held one handle of the cup as it was hoisted aloft after the Blues' historic 2-1 victory over Liverpool, their fourth triumph in the last six finals.
The win also saw Terry become the first man to captain the same club to FA Cup glory four times.
But if Chelsea beat Bayern Munich in the Champions League final on May 19, the honour of being the first player to skipper them to the ultimate prize will go to Lampard, with Terry suspended for the Allianz Arena showpiece.
UEFA have confirmed Terry would be allowed to lift the European Cup and asked if Saturday's routine would be repeated a fortnight later, Terry said: "Let's hope so.
"We did it when we did the double (in 2010).
"I said to Frank: 'Moments like that go down in history', and it's important myself and Frank were there when we did the double."
Terry hailed Saturday's result as the "perfect" boost ahead of Chelsea's showdown with Bayern and the ideal response to the critics who wrote them off before caretaker manager Roberto Di Matteo's remarkable rescue act began two months ago.
Terry said: "People wrote us off midway through the season as well, questioning the togetherness and questioning people's form within the squad.
"Especially when the backs have been against the wall, it's been really good."
No club has dominated the FA Cup in the modern era like Chelsea, with only Blackburn and Wanderers' records in the competition's infancy bearing comparison.
Terry said: "In the modern era, it's virtually untouchable, really.
"The hunger in that dressing room as well to have that feeling, the memories and photos and videos from after the game, is what spurs us on year after year.
"People can question all they like but the hunger in this squad is incredible and that's what keeps us going."
Terry also appeared to suggest his own record-breaking exploits had justified his decision to stay at Stamford Bridge when Manchester City tried to break the bank to sign him three years ago.
"Incredible achievement, and my loyalty to Chelsea has now paid dividends, as always," he said.
"I'm very privileged to be at a club like Chelsea, and to have the armband as well for many years, and to lift these great trophies that I dreamed of as a boy."
That Terry was able to do that on Saturday owed everything to another Wembley goal from Didier Drogba and one of the great FA Cup final saves from Petr Cech.
Terry said of Drogba's record-breaking fourth cup final goal: "You look at big players like him and Lamps, when it's on the big occasions, they always step up to the mark and he's done it once again."
He added of Cech's wonder-save from Andy Carroll, which sparked another 'ghost goal' debate: "Pete's made a great save - let's not take it away from him - probably one of the best saves in an FA Cup final."
Terry was adamant the whole of the ball did not cross the line but admitted the clamour for goalline technology had become deafening after a second controversial cup tie in succession.
"Obviously, there is going to be talk of goalline technology again," Terry said.
"I'm sure they're looking into it and trying to bring it in as quickly as possible."
Terry was also confident the right decision would be made over whether Di Matteo would be appointed Blues boss on a permanent basis.
Terry, who said on Friday he hoped an FA Cup win would help the Italian land the role, added: "With this result - and we're going into the Champions League final as well - it can do him no harm at all.
"On behalf of myself and the other players, he's been excellent."
Di Matteo's ecstatic celebrations were on a par with those after Chelsea's incredible Champions League comeback against Napoli as the 41-year-old joined the select list of those to win the cup as both a player and manager.
Terry said: "He's obviously had some great memories himself in this competition as well, scoring goals and lifting trophies.
"He sat back and the lads were dancing about and he said: `Take it in', and that's what we did."