United went ahead in the 61st minute at Vitality Stadium when Bruno Fernandes converted from 12 yards following Alex Jimenez’s shirt pull on Matheus Cunha.
The visitors then felt aggrieved to be denied a second spot-kick after Amad Diallo went to ground under a challenge from Adrien Truffert, moments before Cherries captain Ryan Christie equalised.
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James Hill’s own goal quickly restored United’s lead but Bournemouth claimed a point nine minutes from time through Junior Kroupi’s penalty after Harry Maguire was sent off by Attwell for a foul on Evanilson.
Speaking of the incidents involving Cunha and Diallo, head coach Carrick said: “He’s definitely got one of them wrong because he’s given one penalty for us for the same thing that he’s not given one.
“There’s a two-arm grab. The Matheus one he gives, the second one on Amad he doesn’t, which I think is almost identical, really.
“If you have two hands on someone in the box and they go over and they’re in control of the ball, for me it’s two penalties.
“It will be interesting to see which one they acknowledge is wrong: the one we got or the one we didn’t get.
“It’s a huge moment. They don’t give it, they go down the other end and score and then it becomes all of a sudden, ‘oh, it needs to be a bigger penalty to overturn’, just because they scored, when actually it’s a penalty and it should be a penalty if you’ve already given one.
“It’s baffling really to make sense of that. And because they score, the game flips a little bit and changes.
“We defended with the 10 men after all that very well. But the penalty one is just astonishing, I have to say. One of them must be wrong.”