Former England and Chelsea defender Terry became assistant boss at Aston Villa following the appointment of manager Dean Smith in October.
Villa defeated Lampard's Derby 2-1 in Monday's Sky Bet Championship play-off final at Wembley to end their three-year top-flight absence.
Despite enjoying early success in the dugout, Terry is content to continue learning as a coach before taking charge of his own team.
"In the long run that's obviously my ambition but I'm not thinking that," he said.
"I've said as a player I got to the heights I wanted to get to and I firmly believe I'm a YTS (Youth Training Scheme) again.
"I'm starting right from the very bottom, I'm not afraid to say that, I'm not afraid to do all the dirty work, picking up the cones, the balls, the bibs, that's part of my education.
"I've got a great teacher in Dean so I'm very fortunate to be able to sit there and learn.
"I've always wanted to do it (coach). I think you know as a player when time's up really.
"It's been something that I've been planning for a few years, and the experience and day-to-day work on the training field and what the manager allows me to do has been fantastic for me."
Both Terry and Lampard have been touted as future Chelsea managers.
While Villa revelled in Wembley glory, Lampard's first season in management ultimately ended in disappointment.
Terry, who won three Premier League titles and the Champions League alongside Lampard at Stamford Bridge, has been impressed with the former midfielder's impact at Pride Park.
"It's been incredible what he's done there at Derby, I don't think anyone would have put them back in the play-offs or anything this year," said Terry.
"He's brought a great team spirit, he's obviously got a wealth of experience, he's got Jody (Morris, assistant manager) who's got a lot of experience in coaching as well.
"It's just great to see young managers - Stevie (Gerrard), Lamps - getting the opportunities."
Terry's final game of an illustrious 20-year playing career came for Villa when they were beaten by Fulham in last season's play-off final.
The 38-year-old feels the pain endured 12 months ago helped the club make amends.
"It's probably served us well a little bit and that disappointment of experiencing going through that, playing at the big stadium, the atmosphere," he said.
"Probably 90 per cent of the group went through that last year, and the emotion.
"It's tough for Derby to take because they've been great but it's great to be on the winning side and back in the Premier League."
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