Both players saw red in the first half of a fiery contest, with Clarke-Salter the first to go on 24 minutes. The young centre-back flew into a challenge on Traore and Coleman admits the occasion perhaps got to the 20-year-old.
Middlesbrough's numerical advantage lasted just 13 minutes as Traore then saw red after shoving Bryan Oviedo off the ball.
Coleman said: "Both were red cards. I can't have any complaints - the referee got it right on both counts.
"You can't raise your hands and do what [Adama] did. I don't have an argument with our red card, it's a red card, and I think their's was too.
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"Jake Clarke-Salter knows he can't tackle like that, and I think the game and the tempo maybe got the better of him. He's a cracking boy, a great kid, but he got that one wrong.
"And you can't raise your hands to anybody. If you do, you're off - that's it.
"I thought we were hampered more. I know Traore is an exciting player for them but the way it was going for us, we were 1-0 up and not in any difficulty. Jake Clarke-Salter has been doing very well for us but we lost him and had to change formation so I think it suited them more than us."
Middlesbrough manager Tony Pulis suggested that Bryan Oviedo had poked Traore in the eye, sparking the furious response from the winger.
Coleman was doubtful of that claim.
He said: "I've looked at that. I think Bryan has put his arm around his shoulder, but it's hard to see from the angle.
"I've seen it [the Oviedo and Traore incident]. He had his arm around there. But poke in the eye? He'll need a long arm to get around to his eye, I've seen the angle and I'm not sure it's [possible]."