Gareth Bale, matchwinner in the 2-1 first leg win, missed a sitter in the second half, but Mousa Dembele saved the Welshman's blushes with a brilliant last minute strike from 25 yards.
Spurs will now face Inter Milan - the team against which Bale pulled out two career-defining performances two seasons ago - in the third round next month, and Villas-Boas said: "We had two magnificent games against Inter and we just want to recreate a special night that everyone remembers at the club."
He went on: "Going through against Inter Milan and Lyon puts you in a good place to win the competition."
Lyon fans will find it hard to believe that it is not they who are facing the Italian giants in the next round.
Tottenham could barely string a pass together in the first half, with Dembele, Scott Parker and Kyle Walker all guilty of poor performances.
Bale also made a mistake in turning his back to Maxine Gonalons, allowing the Frenchman to convert Clement Grenier's cross in the 16th minute.
"We didn't play well in the first half," Villas-Boas conceded. "In the second half we were the better team. We created some chances and we were rewarded with the second goal in the end. "Individual players make a difference and Mousa certainly made the difference tonight."
Dembele's strike, which came after he glided past Grenier and beat Remy Vercoutre with a long-range missile, clearly delighted Villas-Boas who jumped for joy when the ball hit the back of the net.
"It was good," he said. "When you score in the last minute, there are all sorts of emotions going through you, especially with a goal that brings you into the next round."
Source: PA
Source: PA