Ben Chilwell and Kurt Zouma struck, with Jorginho also scoring twice from the spot.
Lampard remarked: "Not too many put four past Crystal Palace. First half we started well, we came off it a little bit. We needed a bit more. It was great for us to get four goals.
"Just the urgency of our game needed more. We needed to get Ben Chilwell into the game. We can't allow Palace's back four to say dealing with Chelsea's front line was easy.
"Ben Chilwell was fantastic today. His ability to be so high up the pitch, and that's not a bad thing, and his great quality on the ball. The lads who have come in have all had issues so we need to give them time but Ben has shown what he's all about.
On Tammy Abraham wanting to take the second penalty, Lampard insisted: "It's been dealt with. No problems. Just dealt with. I want leaders - and a little bit of conflict. It's good that Tammy was enthusiastic but you don't jump ahead of the list."