Entertainment was in short supply at Old Trafford despite the victory but Mourinho chided the home fans for not supporting his players loudly enough.
However, one genuine positive for United was the performance of Chile international Sanchez, who shone brightest on an afternoon on which Huddersfield were not shy in targeting the slightly built Chilean.
Yet despite watching his new signing get repeatedly clattered all afternoon, Mourinho said the goalscorer could handle it as United reduced the gap to Manchester City at the top of the Premier League to 13 points
“Alexis is a fantastic player but not a prima donna,” Mourinho said.
“He’s a humble guy who doesn’t forget where he started and I’m pretty sure when he was playing in Chile he had difficult places to play with difficult performers and he’s quite used to it.”
Apart from Sanchez’s brilliance, the other talking point at Old Trafford was Mourinho’s decision to drop Paul Pogba following United’s damaging defeat to Tottenham Hotspur in midweek.
Mourinho said there had been no falling out with Pogba but he has risked annoying United’s fans after again criticising the volume levels inside Old Trafford.
After first ticking off supporters following a home win against Leicester back in August, and then in programme notes before a clash with Everton a month later, Mourinho again felt the need to point out that the Old Trafford crowd is big, but shy.
“It’s not Portsmouth,” he said. “I remember Portsmouth in the Premier League. It was such a small stadium that the atmosphere there was incredible. Here the atmosphere is a bit quieter, ours is not very enthusiastic but the players love playing here.
“Paul is a fantastic player and no doubt for me one of the most talented players in the world but to sit on the bench for one day is not the end of the world.”
Mourinho also used his post-match press conference to confirm that Marouane Fellaini is likely to be out until March after knee surgery.
Ahead of kick-off, there was an impeccably observed minute’s silence to commemorate the 60th anniversary of the Munich air disaster, which falls on Tuesday, before the first half ended goalless after a physical Huddersfield team did all they could to keep United out.
Most of their tackles were borderline legal as Sanchez, Juan Mata and Antonio Valencia were all roughed up while one challenge on Scott McTominay was particularly harsh.
Sanchez got into the game more as it progressed and tested Jonas Lossl from 20 yards but David Wagner’s side were determined to play for a point and often had all 11 men behind the ball to frustrate the home team.
However, after the break, Huddersfield’s resistance ended, when Mata delivered an inch-perfect cross for Romelu Lukaku, who volleyed home from close range.
Midway through the second half, Sanchez was clumsily fouled by Michael Hefele on the edge of the box and although his initial spot kick was saved, he calmly followed up the rebound to finish off Huddersfield as they fell into the bottom three for the first time this term.
“We wanted to be stable and compact and frustrate Man United for as long as we could,” Wagner said. “Unfortunately, that was not long enough. Defensively I saw everything I wanted to see and work ethic, desire and togetherness.
“Unfortunately we were not able to create defensive moments. In the end it was a fair result.”
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