Paul Trollope said: "We were beaten by the better team tonight.
"Losing Rickie so early in the game was a huge blow to us, he's been the platform and the link of our lay. That was a bitter blow on top of the strikers we were already missing.
"Rickie had experienced a bit of tightness but we thought he'd be fine, and he started the game in a bright manner.
"It made it harder for us to build our attacks in the forward areas. We still felt that we were pretty solid despite Derby's possession in the first half.
"It was disappointing to concede the goal early in the second half, they had a lot of passes in the build-up and we could have put the pressure on earlier.
"The events of today (Nigel Pearson's suspension) maybe gave them a freshness, it was a difficult evening for us."
Paul Trollope defended Kenneth Zohore after a difficult evening for the substitute and thanked fans for sticking with the team.
He said: "Kenneth's a young player who is still developing, he's still very much learning the game.
"It was a big ask for him in a difficult situation.
"I'm not one to make excuses, you still have to believe you can cope with the opposition. For large spells of it we did that, but we didn't look too likely in open play and didn't build up a huge head of steam."
Trollope said Lambert would be assessed after the game with a hamstring injury and that 'fingers were crossed'.
"I believe I will be in charge on Saturday against Reading, I will speak to the owner on Wednesday and we will go from there," said caretaker boss Chris Powell after he took charge of Derby when they suspended manager Nigel Pearson before the game at CCS.
"But that was Nigel's team and I dedicate that win to Nigel because I felt it would come and he had them in the right place to perform and full credit to everyone at the club after a tough 24 hours.
"It is very emotional. I thought the players were extremely professional, it would have been easy to go the other way because of what has happened and fail to perform.
"They were terrific, I am really proud of them and the fans who came all this way, it has been a tough start but we know the quality we have.
"We have had tough results but I always felt the players would perform after how they trained."