West Ham consider themselves the Academy of Football and, as director of the youth set-up, Carr has overseen the development of seven current England internationals.
Cole has always remained popular with the West Ham supporters but Terry and Lampard received an unusually positive reception at Upton Park.
The few boos that rang out were soon drowned out by applause.
Terry said: "Unfortunately with what is in happening in the Premiership we were not able to go out there and play tonight but myself, Frank and Joe are here supporting Tony. He was a massive part in our upbringing at the football club.
"The crowd did give us a great reception. It was totally unexpected. It is not the kind of response we get when we come here with Chelsea of course but we are really grateful because it is all about Tony Carr tonight.
"It was nice for all three of us to get a great reception from the fans. More so for Joe and Lamps because they have played in the first team here and a lot of games but even for myself it was still very nice. I appreciate it.
"The fans will all be cheering us on in the summer (at the World Cup) and I know they will be right behind what we are trying to do for the country."