Goals from Samuel Eto'o and Gary Cahill in the first half on Tuesday earned Jose Mourinho's men a comfortable 3-1 aggregate success as Chelsea progressed to the quarter-finals of the competition for the eighth time in the past 11 seasons.
Much was made prior to the game of the return to Stamford Bridge of Didier Drogba, but the Ivorian had very little impact in the second leg of the last 16 tie.
Lampard, who had a hand in Chelsea's second goal, declared himself satisfied with his team's professional display.
"It was everything we wanted it to be," he told ITV Sport.
"It was a tough game, people take it for granted after our good result there. We knew it was going to be tough but beginning to end they hardly threatened.
"It was very controlled from all of us."
Lampard also hailed former team-mate Drogba, but the midfielder is not looking too far ahead in terms of Chelsea's future Champions League prospects.
"We know what Didier is about, he's top class and we had to be on our game," he said.
"I won't make predictions yet with the amount of great teams still left in it.
"We'll see who we get drawn against. It gets tougher every year this competition but we're in the draw."
Mourinho, meanwhile, insisted that Chelsea are back where they belong after last season's UEFA Europa League success under Rafael Benitez.
"We are there," he said.
"It's different from last season because the Europa League was a different level but to come from Europa League to the quarter-finals of the Champions League is important for players and for the club.
"We are a Champions League club, we are in the best eight, among the best teams in the world and the players deserve to be there."
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