The Armenia international was brought on at half-time during the Red Devils’ shock 2-1 defeat but failed to inspire a comeback from Mourinho’s men.
Mkhitaryan started the game on the bench as Mourinho opted to ring the changes for the Premier League clash.
Marcus Rashford’s second half goal was not enough for the Red Devils as they suffered their first defeat of the season with a 2-1 reversal against the newly-promoted team.
And explaining his team selection choices before the game, Mourinho told Sky Sports: “There are four changes in the team to try to give a bit of fresh legs and intensity.”
Manchester United’s defeat by Huddersfield left Mourinho’s men five points behind Premier League leaders Manchester City after nine games of the new season.
The Red Devils will aim to get back to winning ways in the top flight when they take on Tottenham Hotspur at Old Trafford next weekend.
Mourinho is aiming to become the first manager to lead Manchester United to the Premier League title since Sir Alex Ferguson’s final campaign in charge in the 2012-13 season.
The Red Devils finished sixth in the table but won both the Europa League and League Cup last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news