Goals apiece from Mateusz Klich and Ezgjan Alioski -plus a Kemar Roofe’s double – saw Leeds overcome their hosts.
Derby’s sole comfort was a stellar strike from Tom Lawrence early in the first half.
But Lampard, who tasted his first defeat as a manager at Pride Park, says he knows where the Rams went wrong.
“It was tough,” he said. “We were well beaten by the better team on the day.
“More energy in them without the ball and with the ball.
“There were a lot of lessons for us.”
Leeds United were 2-1 ahead by 18 minutes but turned the screw in the second half to take the three points.
Lampard added: “To be fair, Leeds have come to our place and looked more confident than us.
“They played very well but if you get your game right and work hard, you should be able to deal with these things.”
Next up for Derby is a trip to Oldham in the Carabao Cup on Tuesday, before a return to league action with a visit to Millwall next Saturday.
“We didn’t perform at our abilities, in terms of our mental attitude again,” Lampard added.
“When things get tough you have to stick to your guns, which is what we didn’t do. They moved the ball better, we made mistakes which gave them goals.
“There wasn’t one reason why they were better.”