The United interim boss suffered the first loss of his interim spell as the Red Devils were beaten 2-1 by the 10-man Magpies in the Premier League on Wednesday (04.03.26) and thought that his team's performance wasn't up to scratch.
Speaking to TNT Sports, Carrick said: "We are not happy the way we played tonight. The way the game panned out we had it in our hands largely but credit to Newcastle and they way they approached it, we knew it would be tough but we navigated the game to a position where we could kick on but we didn't. Bitterly disappointed really.
"I don't think it was the 10 men, we just didn't play good enough. We can't make excuses for that. We all take responsibility for that.
"It was just the quality of the performance, it wasn't character or wanting to win, it's easy to throw that just because you don't win a game of football
"Newcastle deserved to win tonight, it hurts me to say that. That is how it was. We need to get back to work and be better for the next game."
Carrick stressed that United remain in a "decent position" in their quest for Champions League qualification and urged the team to put the setback behind them.
He said: "We've lost one game, we haven't played well enough but in the grand scheme of things we are in a decent position. Tonight hurts but we will be better for the next one.
"You have to get back at it, work hard and do the things we did to win the games we've won. We can do that, we are a good team, tonight wasn't for us.
"We have to learn from it and get better for it. We had a lot of praise lately and the boys deserve it, this doesn't change how we approach the next game. We've got everything to play for."