United's interim manager Michael Carrick branded Attwell's decision-making "baffling" and "astonishing" in his post-match press conference.
He said he had not spoken to Attwell after the final whistle and will take no comfort if PGMO admits a mistake was made.
"It's kind of, once it's done, it's done," said Carrick. "You can have all the conversations in the world about could it have been this, could it have been that?
"I just think that's for VAR. If they've already given one and agreed that that was a penalty, then surely the next one should be a straightforward one? After it, there's no point, whatever comes. Whether they apologise or not, it's done now."
United remain in a strong position in terms of Champions League qualification but victory would have seen them close the gap to Manchester City to four points ahead of the international break.
The draw with Bournemouth means United have only won two of their last eight games away from Old Trafford despite the upturn in form under Carrick.
"In this league, it's tough to win games," said the former Middlesbrough boss. "We've won a lot of games recently so the amount of points we've accumulated and some of the performances and the results we've had I think is a big positive.
"Home and away, it's a tough league and it happens. You've seen how games can unfold quite quickly but I thought we managed it in the end pretty well."
