Clarets boss Sean Dyche had an ounce of sympathy for Derby, but felt his side were deserving of the points.
Burnley were leading 1-0 through David Jones’ first league goal of the season, when County striker Chris Martin received a second yellow card and subsequent red for simulation in the area under a challenge from Kieran Trippier.
The Rams felt hard done to, and the Clarets went on to complete a 2-0 win with a Dean Marney effort after the break.
Dyche said: “I thought first half we were very good again I thought there was a nice feel about the group, great energy and a real quality feel about us.
“We shifted the ball well, created chances and I felt we deserved to be up in the game at half-time.”
On the sending off, he conceded: “I think it’s fair to say you would be disappointed, but the boy Martin had been involved in five or six incidents before that, and the referee has had to book him.
“He could have been booked before that.
“I think he slips, but he appeals instantly which always puts doubt in the referee’s mind.
“I can imagine they would be disappointed, and I probably would have been, but I felt we were in good shape before that, and probably better 11 v 11.”
Jones’ strike was one to savour, and Dyche said: “Jonah’s got quality and it’s a great finish, it was a great move building up to the finish as well.
“Deano from a set piece as well, that’s good value to us, we work on them and it worked for us.”