United had Harry Maguire sent off, while the visitors also felt Amad Diallo had a deserved penalty waved away.
Carrick said afterwards: "Disappointed - we created enough chances and had enough opportunities in the game. A big opportunity to go 2-0 up and we get one penalty and not the other.
"It's exactly the same thing really - a two-handed grab. He's (referee) got one wrong so, I don't know which one but he doesn't give us the second one. I think they're both penalties and it's a massive moment in the game and it ended up chaos after that. Massive moment and I don't understand how you can give one and not the other - it's crazy.
"It's as obvious as you can get - you've already given one so to not give the other one. It's clear, if that's what he believes is a penalty to start with then the second one has to be. I don't understand how you can't give that. And then the goal and after that it was chaos. I was really pleased when we went to 10 men we saw the game out and took a point that's a real positive. In the end the way it went you can lose those games so to take a point int he end we'll take that but disappointed not to take all three."
Asked about Maguire's dismissal, Carrick said: "Maybe (it was harsh) - it ended up chaos at that time so decisions go in different ways and he's made that decision. Ours should've been a penalty before, we would've had two penalties and then that wouldn't have happened.
"Credit to Bournemouth the way they play - really energetic and positive and constantly test you. To go with 10 men for so long and having to make changes, the boys off the bench finishing the game did really well. Delighted with that seeing off the last moments that could've been really difficult but we coped well."
On the international break before next game, he concluded: "It is what it is. It's not a problem. Boys are going away and it feels a lot because of the international break but we'll be ready for Leeds when it comes."