The Reds' players watched Manchester City triumph 2-0 at Newcastle thanks to second-half goals from Yaya Toure and, although the goal difference between the two challengers remains the same after the day's events, at least United's win means the champions still have a chance if QPR cause a huge upset at the Etihad Stadium next Sunday.
"We watched it anyway before the game," he told MUTV. "You can't hide from it. It's only natural that we were hoping they slip up but obviously City have won the game so we had to get our heads on our game and, credit to the boys, we kept believing and we still believe anything can happen. It's not over. We'll keep believing and take it until next week.
"We created a number of opportunies," Carrick added. "We wanted to start quickly and get on the scoresheet quickly and build from there. We did that but didn't take our chances, although we'll take a win that gives us an opportunity to take it to next week. It would've been a big ask to score six, seven or eight goals. We tried but we couldn't in the end so we'll take the three points.
"In an ideal world [we'd have scored more] and we could've been three or four up at half-time so who knows after that? That was the aim but it didn't quite work out."
Carrick stressed that United are focused on winning the final game of the campaign at Sunderland, regardless of worrying how City will fare against Mark Hughes' QPR.
"We can still hope," said the midfielder. "It's up to them now. We've got to go there [to the Stadium of Light] and win. It's still a tough game and