Sunderland boss delivers verdict on controversial decisions in six-goal thriller with Middlesbrough
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.
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Hide AdMiddlesbrough'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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Hide Ad"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."
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Hide AdMiddlesbrough 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]."