The Red Devils scored three times in the second-half in the 4-0 victory at Old Trafford.
Lampard was happy with parts of the Blues' performance, but lamented their inability to stop United's blistering attack.
He said: "At 1-0 we were the better team, but I can't stand here and look happy with that because it's 4-0.
"This is a counter-attacking team [United], a big strength of theirs. We know they have pace, if you turn over the ball or give them opportunities to play in behind, they will.
"For large parts of the game we didn't [let them] do that, we were the ones who were bright, breaking, the last bit [in the final third] wasn't great, but we were so comfortable in the way we were playing in the first half, so there are loads of lessons for us."