Derby hadn't dropped a point this season but were beaten by two Charlie Austin goals, but the 'young man' in charge of Derby, Nigel Clough felt they deserved much better.
"There are ways to lose and today, in the second half, we played exceptionally well," Clough said after the game.
"I think that was as well as we have played this season, apart from the second half at Blackpool. We created chances, had a few off the line and I think we deserved something out of the game today.
"The lads gave it all they had, which is all we can ask from them, and we experienced the fine line between winning and losing. We needed to keep it tight after equalising, but it wasn't to be for us. We needed a break that didn't fall our way today.
"Both goals we conceded could have been avoided and I think our inexperience showed at times. We hadn't given anything away in any of our first four league games, but today we contributed to the goals we conceded, but we will learn from it."
Clough added: "We are delighted with 12 points and I don't want today to diminish how great the players have been for us. No one gave us a cat in hell's chance of getting 12 points from 15 a few weeks ago, so we're delighted with the return we've got from a very honest bunch of players."
It might have been Derby's first dropped points but it was Burnley's first league win and manager Eddie Howe was a happy man at the final whistle. "It was a fantastic win, first and foremost because we needed a result and the lads really performed," he said.
"With extra time in midweek it was always going to be a tough ask coming here, but we had the best chances of the game and in the end could have won by more.
"The last 20 minutes was back to the wall and we really dug in and showed another side to our game. It seemed like a lifetime and by the time he signalled for seven minutes of stoppage time it seemed to be getting longer by the minute.
"Time goes so slowly, but this is a great win and it gives us confidence to go forward, so I am absolutely delighted with the lads.
"We are a work in progress, but the thing that pleased me most today wasn't the football we played. It was that resilience we showed and the team spirit. You could see that even with the subs coming on, absolutely desperate to win the game and throwing their bodies on the line and helping each other.
"That's what we need. Everyone is in this together, the whole squad, staff and the fans. We all want to take this club forward and try to be successful"
Having gone in front once, Derby equalised before a second Charlie Austin goal won it for us. "You feared for us when we conceded, especially after midweek, because the lads looked fatigued," Howe admitted.
"But we found another burst of energy from somewhere and Charlie has got another two goals for us. Both he and Jay played very well together and the fitter Charlie gets the better he looks. I thought he led the line well and the great thing is he looks razor sharp in the box.
"Derby play three in midfield and we didn't want to be too open coming here, so we dropped Jay just off Charlie and played a little bit tighter. I felt it suited us better away from home and hopefully we are on the right road."
Howe had made two changes to the team that had played last Saturday and one of them was in goal where Brian Jensen was recalled and the manager said: "Brian did very well. It was a good comeback for him and it was a difficult decision.
"I am lucky to have two fantastic goalkeepers who are both number ones, but I felt I needed to make a change. That's nothing on Lee, but Beast is a fantastic goalkeeper and to have him back between the sticks was good today because I felt he commanded his area, came across for crossed and was there when we needed him."