Gilmour, 18, was chosen to play alongside Ross Barkley and Mateo Kovacic in the heart of the Chelsea midfield and helped the Blues to a 2-0 victory in their fifth round FA Cup match.
- Willian and Barkley help Chelsea knock Liverpool out of cup
- Billy Gilmour and the curious case of the hype machine
Speaking after the game, Lampard was full of praise for the Scottish youngster.
"What an incredible performance for a young player," he said. "He was a calm head in that first five or 10 minutes.
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."
Barkley, who scored Chelsea’s second with a fabulous solo effort, echoed his manager’s comments.
"Billy was brilliant. But it was not a surprise to me. I've seen him in training and he was like that in training last season."
Barkley went on to add how special it was for him to score against Liverpool as a boyhood Evertonian.
"It was brilliant, a massive result for the lads. We needed a top performance tonight at home after two disappointing results.
"Scoring against Liverpool is massive for me. As an Everton fan, it's always a dream to score against them.”
One notable selection change from Lampard came in goal with under-fire Kepa Arrizabalaga starting between the sticks and put in an excellent performance.
Lampard hailed the mentality Kepa showed following some high-profile mistakes.
"I was really pleased for Kepa.” Lampard said.
“It's not easy because all players want to play and a goalkeeper gets scrutinised more than any other position and he made some good saves.
"He's shown good character and he played well."