Lampard saw Leeds pull his team apart with pace and movement as his first home game in charge ended in a chastening defeat.
The quality of Leeds movement forward caused Derby problems from the start and it was no surprise when Mateusz Klich fired a low shot past Scott Carson in the fifth minute.
Tom Lawrence equalised with a 12th minute free kick that Bailey Peacock-Farrell should have saved but Leeds responded by retaking the lead through Kemar Roofe's header from Ezgjan Alioski's cross in the 21st minute.
Derby had a bright start to the second half with Mason Mount dragging a shot wide but Klich set up Roofe to beat Carson with a rising drive on the hour before Alioski headed in Pablo Hernandez's cross four minutes later.
Lampard made no excuses and said: "It was tough, we were well beaten by the better team on the day. We went into the game under no illusions and knew it would be difficult for us.
"There were no surprises but we didn't deal with them. They are a good team, had more energy with the ball and without it so lots of lessons for us really.
"We can't get too down because we are two games in and there's a long, long way to go but lots of lessons we must improve on. The most disappointing thing for me is we went away from what we are.
"Leeds have come to our place and looked more confident than us. it comes down to the basics of football, if you don't move the ball quickly enough and you're not brave enough and your quality is not quite good enough then it's hard to get out and we weren't good enough today.
"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. I'd rather people take a chance and try and play out in a positive manner than not so great lessons for us today."
Leeds manager Marcelo Bielsa, speaking though an interpreter, said: "It was more clear during the second half but in the first half we suffered some actions that could have allowed our rivals to score goals.
"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.
"Derby County has good players and a head coach that will allow the team to play an important role during the Championship. But what happened in the games so far does not mark a definite trend, it's too early to make conclusions.
"In each game we will have to prove again so this is a competition where you have to show regularity. So it is very important to bear this in mind.
"I always think about the continuity and regularity of the performance, this is the most important thing because during a competition you have ups but you also have downs.
"But the performance of the team was better today than last Sunday, the performance of some players lasted longer."