Lampard's side have now lost twice in succession in the Championship, having conceded twice in the first 21 minutes during their 4-1 defeat by Leeds United.
"We knew what to expect from Millwall," the Chelsea legend told Sky Sports News. "They are very effective at what they do.
"We deserved a draw. But it's always difficult when you are 2-0 down, because you become desperate as the game goes on. I'm not pointing fingers, we knew balls were going to be firing into our box, but as a group we need to deal with them and clear them.
"There is a bit of a lottery with Millwall, you can try and win the lottery by getting close to people by clearing your lines and digging in. This atmosphere in this stadium is one of those that when with the home team - it is massive."
Derby return to action on Tuesday night with a home game against Ipswich Town.