The Scotland international goalkeeper was given his marching orders for the second time this season in controversial circumstances on Wednesday when he upended Mohamed Diame midway through the first half in West Ham's 2-1 win, but referee Mike Dean initially saw nothing untoward.
Dean then pointed to the penalty spot three minutes later after a consultation with his assistant and McGregor was shown a straight red card when he got to his feet following lengthy treatment after he came off worse in the collision with Diame, who appeared to handle the ball before contact was made between the pair.
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Mark Noble scored the resulting spot-kick and, although Hull equalised when Tom Huddlestone's free-kick went in off Nikica Jelavic, a James Chester own-goal consigned the visitors to defeat at Upton Park.
Bruce revealed after the game that former Rangers keeper McGregor had been taken to hospital and the club are awaiting further news as to the extent of his injury.
"Unfortunately he's in a bad way, he's certainly got kidney damage," the Hull boss told reporters.
"The specialist is on his way to see him. He's got contusion of his kidney, which we are hoping is not ruptured, but it looks a nasty one at the minute.
"He's in hospital and he'll remain in hospital overnight."
Bruce also expressed his frustration at a "calamity of errors" from referee Dean.
"I'm not going to give you the stories you want, because I've paid enough this year in fines," he added.
"If the referee had given the penalty straight away I could understand, but he didn't and we've got video evidence of that.
"I asked him if he'd given the penalty and he said he did.
"It must have been two or three minutes before he made the decision, so if he has given the penalty, we've obviously got somebody on the line to clear the ball, so it's not really denying a goalscoring opportunity.
"Is it not sufficient to say, a bit of common sense, if he thinks it's a penalty - which he didn't at the time - then just give the penalty and let us play with 11 men.
"I'm convinced if we play with 11 men we take something from the game, with 10 men I still think we're the better team, with 11 obviously that would have been easier.
"He's missed a blatant handball, so it's a calamity of errors but what makes it worse is if he gives the decision okay and he's not too sure, then how does he send the player off?"