Mitrovic was dismissed for an apparent stamp on Francis Coquelin just 16 minutes into the clash, with Andre Marriner brandishing a straight red card.
It followed a third minute booking for Moussa Sissoko, while five other Newcastle players were booked throughout a physical clash.
McClaren felt referee Andre Marriner was too keen to book his players for their overzealous tackling, resulting in the official ‘making a rod for his own back’ when faced with a decision on the striker’s foul.
“It was harsh,” McClaren told BT Sport. “It was more clumsy. His eye was on the ball and he kind of stood on his foot.
“We saw Moussa Sissoko’s one just after which got a yellow card; it was similar.
“I don’t want to criticise but I just felt early on there were too many yellows and he (Marriner) kind of made a rod for his own back where he had to keep producing them. They were fouls and we’re not disputing that.
“Our boys are young and innocent, they stay on their feet, they don’t roll over, they don’t fall down easy and we just felt we were a victim to that.”
Nevertheless, McClaren was full of praise for his players, who, despite creating few goal scoring opportunities of their own, restricted Arsene Wenger’s side to a scrappy own goal from the unfortunate Fabricio Coloccini.
“All we could do after that was show spirit, fight and discipline, and they were magnificent in terms of that,” McClaren said.
“What a fantastic crowd as well. When we get 11 players on the field and we get a decent game this crowd is going to roar us on.
“After four games we’ve been down to 10 men in two of them. Harsh, definitely, but we need to learn from that.
“I couldn’t fault them. We want to be a team that’s hard to beat. I think we’ve done that, even being down to 10 men for 75 minutes against one of the best teams.
“Fantastic spirit and what a crowd. As long as we keep this spirit we’ll get better.”
The recent addition of Florian Thauvin marked the fifth arrival at St James’ in this summer’s transfer window, but former Derby head coach McClaren doesn’t envisage any late deals for his side.
“No, unless I get into the office and Lee Charnley’s got one up his sleeve. I’m pleased with what we’ve got.
“I’m disappointed today, but what a fantastic crowd, fantastic bunch of players and fantastic spirit.”