Brighton took a 2-0 lead into half time after a poor first half performance from Derby, but Ashley Cole got one back in an improved second half and they fell just short of an unlikely equaliser.
Lampard said: "First half we were slow. There was a lack of urgency.
"To come to a Premier League team and give them time on the ball is a cardinal sin. We were waiting for them to score.
"We weren't at the races. Whether it was fear or respect, it wasn't enough to come here and get a result.
"In the second half, we were the team in control and had more urgency in our game. We nearly got ourselves back in it but the first half made it so difficult for us."
Lampard said his side gave Albion too much respect despite his 'clear message' before the game.
He added: "We gave them too much respect. The message was clear that we had to be confident and leave everything here to get a result.
'We had to be really aggressive and work hard off the ball and be confident and comfortable on the ball.
"I don't think we were but the real problem was the aggression of the ball because we allowed them time. Allowed them time to cross for the first goal and allowed them to shift inside and hit the post to get the rebound for the second goal.
"Against a Premier League opposition, that is impossible to get you a result."
Lampard did take positives from former Chelsea team mate Cole's goal.
He added: "I'm delighted for Ashley. He's been working hard.
"He wasn't quite ready for the whole game so we gave him 45. He was calm and assured on the ball, as we know.
"He's got all the experience of his career and then he got his goal. It's really good for us and we will need him."