The Red Devils opened the 2017-18 promising to compete for the English top-flight crown.
They have, however, been unable to sustain a challenge, with Manchester City having opened up a 16-point advantage over their arch-rivals.
That has led Mourinho to admit that the trophy will elude him, but Young insists United will continue to compete for as long as it is mathematically possible to bridge the gap.
"It's about picking up points home and away, picking up wins.
"A lot will be said about the way you pick up points, but when you come to the end of the season, that is the main thing - picking up points - and that's exactly what we will be looking do.
"We have to make sure that we keep winning.
"We say before every game that it is another important game, but every game is important now leading up to this final run towards the end of the season."
United’s next outing will see them focus on Premier League matters, with a trip to Crystal Palace set to be made on Monday.
After that, a grudge match against Liverpool will be staged at Old Trafford before attention shifts to knockout competition and the second leg of a Champions League last-16 encounter with Sevilla and a FA Cup quarter-final clash with Brighton.
Young is hoping to help keep the Red Devils competing on multiple fronts, with there still all to play for approaching the business end of the season.
The versatile 32-year-old added: "We are in a lot of competitions; there are points to play for and cups to play for.
"That's what every footballer wants to do; you want to be in the big competitions to go and have a chance to win them.
"And when we come to the game on Monday, hopefully we will be saying we got the three points."