The game turned in our favour when Boro's full-back was red carded for the two-footed lunge just before half-time.
We capitalised in the second half with goals from Jermain Defoe and Fredi Kanoute.
McClaren said: "I've seen it a few times now and I feel the red card wasn't deserved. We will appeal against it.
"The decision was made too quickly. He didn't have to make it that quickly and, as a spectacle, he spoilt the game.
"I told him that, although I understand being a referee is very difficult and you have to make split-second decisions, I didn't think he had to make that decision instantly.
"He could have taken a step back and I think a yellow card would have cooled everything down.
"The decision has cost us the game. In the first half-hour, we were in control and there was only going to be one winner. Anybody would admit that, with that decision, Spurs got a bit lucky.
"It was a rash challenge, a bad tackle. But it was the first bad tackle of the game. If there had been a bit of niggling or animosity before that, I could have understood it.
"But it must have been the easiest game to referee. There was hardly a challenge and good football out there."
Middlesbrough boss Steve McClaren felt his side were hard done by after Franck Queudrue was sent off for his challenge on Noe Pamarot on Sunday.