Carrick said his side had not given up hope of snatching the title, but admitted they had been deflated after watching City's win before kick-off.
"We were watching game at Newcastle and hoping for something. It didn't quite happen for us," he told Sky Sports 1.
"We had to be professional and to take it on to next week.
"It was about winning the game. Credit to the boys after watching the game before. It can be difficult. We can only hope next week."
"We have to concentrate on ourselves. Sunderland will be a tough game.
"We still have a chance of winning the league."