United missed the chance to move within two points of fourth-placed Manchester City as they played out a 1-1 draw against 10-man Leicester at Old Trafford on Sunday.
But with City subsequently losing at Southampton and United still having a game in hand, the value of the point grew later in the day.
Trailing by four points, United’s fate may no longer be entirely in their own hands but an opportunity to strike could open up next weekend if City slip up again against third-placed Arsenal.
Asked if all was still to play for, midfielder Carrick said: “Of course. We will keep going. We have got the games left.
“We will just look to the next game now and try to win that. That’s the only thing we can control and that is what we have got to focus on.”
Carrick, however, did admit frustration that United could not see off Leicester.
Despite the Foxes’ outstanding season, Carrick felt the Red Devils let two points slip.
United had gone into the game on the back of their exhilarating last-gasp FA Cup semi-final victory over Everton and having won six of their last seven league matches.
“We were certainly looking to win the game,” said the 34-year-old. “It was an opportunity for us to build on what we had gathered over the last few weeks, so we’re disappointed with a draw.”
United started well and took an early lead through Anthony Martial but Wes Morgan soon levelled.
Carrick said: “I thought we came out very well and put them under a lot of pressure and caused them a lot of problems. We got a goal ahead and then their goal came out of nowhere. We are disappointed with that. It was a cheap goal to give away in the position we were in. That is hard to take but I thought we played well.
“They put so many numbers round the edge of the box and defend deep, and there is not much space to play through but, especially early on, we played quick and caused them problems. Then there is the threat on the break but, all in all, I think we nullified that.”
United now face a tense end to their league campaign with their trip to West Ham, another of their top-four rivals, a critical fixture on May 10. That game – the Hammers’ last at Upton Park – comes between United’s other two remaining fixtures against Norwich and Bournemouth.