Former England global Lampard won his first game as manager 2-1 against _ thanks to a last-minute victor, but couldn't repeat the trick in his first home game in charge.
From a Lawrence cross, an effort from Craig Bryson then flew wide but at the other end only a fantastic save from Scott Carson denied Roofe a second as the striker's header was somehow kept out from close range.
There was nothing the former England worldwide could do about Roofe's second goal, though, the striker collecting a Klich pass and brilliantly spinning away from two defenders to thunder in a powerful drive that beat Carson at his near post.More news: Paul Pogba posts cryptic message on Instagram after Manchester United win
He said: "We were under no illusions as to how hard it would be beforehand but we didn't deal with what they threw at us".
Derby will look to learn from mistakes against Leeds when they take on Oldham Athletic in the Carabao Cup on Tuesday night before resuming league play against Millwall on Saturday.
"We were well beaten by the better team on the day".More news: Unauthorised take-off of plane near Seattle
Leeds were full value for their 2-1 lead at the break but Derby went agonisingly close to equalising two minutes into the second half when a shot from Mount flew across the area with the sliding Waghorn narrowly failing to find a touch for what would been a tap in.
"When things get tough you have to stick to your guns, which is what we didn't do".
"That's not to say we're not good enough, we certainly are but we need to be braver and can't play longer balls when we should be trying to get out because that's an easy option. In the first half, we were a little bit unstable, we had moments of instability so we can point out this aspect as one to correct", he told reporters. But what happened in the games so far does not mark a definite trend, it's too early to make conclusions.More news: Trump doubles steel & aluminum tariffs on Turkey
"If you play as we did against a team like Leeds when they're on their game, you'll lose".