Carrick 'baffled' by inconsistent penalty calls as Man Utd held
United took the lead from the spot through Bruno Fernandes but were denied a second penalty when Amad Diallo went down inside the box under a challenge from Adrien Truffert.
Bournemouth immediately broke to equalise when Truffert teed up Ryan Christie to level.
A James Hill own goal restored United's lead before Harry Maguire was sent-off and conceded a penalty for bringing down Evanilson.
The contact on the Brazilian striker was remarkably similar to that ignored by the officials for Truffert's challenge on Diallo.
However, VAR did not intervene on any of the calls to ask referee Stuart Attwell to review his decisions.
"To give one and not give the other, I just can't get my head around - it's crazy," said Carrick.
"I can understand that decision (to send off Maguire) but we should have had another penalty and the game would have been different.
"I thought that was what VAR was for, to clear things up and consistency.
"It's two different decisions, so a bit baffling really."
Despite the disappointment of not stretching clear in third place in the Premier League, United remain well-placed for a return to the Champions League next season.
With a top-five finish almost certain to secure a place in Europe's elite competition, they lead sixth-placed Chelsea by seven points.
United are not in action again for over three-and-a-half weeks as an international break is followed by the FA Cup quarter-finals.
"We could have had more tonight but it's not the end of the world," added Carrick.
"We'll come back stronger after the break."