Willian and Ross Barkley scored in each half on Tuesday night to oust Jurgen Klopp’s men from the competition.
Speaking to the media after the game, Lampard said Chelsea have to celebrate beating the best team in the league despite having a long way to go before reaching the final.
"I'm really proud. Liverpool are the best team in the league and what they are doing is incredible,” the 41-year-old said.
“So for us to put in a performance like that, the effort, the quality was something special. We know we've got a long way to go but you have to celebrate those moments."
Lampard’s decision to start Billy Gilmour was vindicated as the youngster was named man of the match following a composed display in midfield.
"What an incredible performance for a young player. He was a calm head in that first five or 10 minutes,” the English man said when asked about the performance of Gilmour.
“He's a throwback of a midfielder. Can you put your foot in? Yes. Can you make angles to play the passes? Yes.”
“He's only slight in stature but he's huge in personality. He deserves people to talk about him after a performance like that."
