Goals from David Jones - against his former club - and Dean Marney saw the Clarets pull five points clear in second place, widening their lead over the third-placed Rams.
Derby's cause was not helped when just before half-time and already 1-0 down, Martin saw red when he was shown a second yellow card by referee Robert Madley for a dive in the box.
McClaren believes it was a penalty however but remains adamant that his side can still beat Burnley in the chase for a top-two finish.
"I've looked at it over and over and it's a penalty. There's slight contact and Chris Martin has slipped because of the contact, his leg has been taken away. It wasn't a dive," he said.
"First thing was he (the referee) hasn't given the penalty which was wrong and then he gave him the yellow card for diving which is wrong again.
"We feel hard done by but that's football. Some decisions you get and some you don't but over the season we have had decisions that have gone our way and some that have gone against us like this that have cost us the game.
"I thought in the second half we were very good, the response was brilliant. We went for the game and the players responded to that. I think that is why the 3,000 fans were still buoyant at the end which was important.
"We're just disappointed that for over 45 minutes the game was 11 against 10."
Jones gave Derby stopper Lee Grant no chance with the opener - a superb half-volley on 29 minutes.
To Derby's credit, they created chances after the break when down to 10 men and both Conor Sammon and Patrick Bamford threatened before Marney prodded home on 68 minutes.
Clarets boss Sean Dyche could sympathise with McClaren over the sending off but believes Martin did himself no favours while on the pitch.
"I thought in the first half we were very good again, there was a real quality feel about us as a side. We shifted the ball well and created chances," he said.
"You don't always get what you deserve but I felt we deserved at half-time to be up in the game.
"I think it is fair to say that you'd be (disappointed with the sending off) but the boy Martin has been involved in five or six incidents before then and the ref has had to book him, could have been booked before that.
"I think he slipped but when he slips he appeals instantly and that always puts doubts in the referee's mind.
"They're going to be disappointed and I think I probably would be as well but I do think we had the better fist of it. We were in good shape but weirdly we were better at 11 v 11.
"We have made this a very, very tough place for people to come."