Lambert received a mixed welcome as he walked out at Carrow Road, with a few jeers heard among general applause for the man who masterminded the Norfolk club's meteoric rise up to the top flight from the depths of npower League One.
However, the former Canaries boss, who is in dispute with his old employers after an acrimonious departure during the summer, enjoyed the last laugh as substitute Andreas Weimann hit a second-half brace to turn the tie around after Brent Holman had cancelled out Steve Morison's opener.
Christian Benteke cracked in a fourth during stoppage time to move Villa within 180 minutes of Wembley.
"I thought we were excellent for the whole game," Lambert said.
"We have been playing like that since the Sunderland game, but I am delighted, I really am."
Lambert, who is been represented by the League Managers' Association in his arbitration hearing with Norwich, which is set for early next year, maintained he will always look back on his time at Carrow Road with pride.
"I had three great years here. We gave anyone a really good run for their money. I love the club. I've got nothing but praise for the football club," he said.
"You like to think they [fans] appreciate what you have done and I appreciate the support they gave us.
"It is great club with great fans, but this is Chris' (Hughton) team now, he has done fantastically well with the position he has got them into and we will try and catch them."