The key incident occurred in the 34th minute when Jesse Lingard took Paul Pogba's lofted through ball down brilliantly before juggling with it in the area, however, was stopped by the arm of Mayo Yoshida.
It would've been a harsh penalty to award, but they have been given and some believe the Red Devils' boss is right to feel aggrieved by Craig Pawson's decision to wave away the wild claims.
Mourinho vividly remembers past penalty denials
United have been denied potential spot kicks on a few occasions this season, and Mourinho wasn't shy to publish his thoughts on another shout being ignored:
“I watched [the incident] from the touchline and it looked very clear to me, but there was 50 metres in distance so I gave the referee the benefit of the doubt.
"I know my players, so when I see people like Juan Mata being hysterical I couldn’t be in doubt, and then at half-time I watch it and it’s a penalty; like Marcus Rashford against Leicester City was a penalty, like Ander Herrera against Manchester City was a penalty.
And he’s unlucky, because honestly, I repeat the three referees’ performances in these matches; [Michael] Oliver against City, [Jon] Moss against Leicester and Craig [Pawson] tonight were good performances. So, unlucky decisions have obviously punished us.”
United did enough to win the match
The result means United's winter winless run has extended to four games, drawing the last three Premier League outings, but José Mourinho thinks his side deserved three points:
“I think we did enough to win. With all the difficulties, I think we did enough to with. At the start of the game we lost a striker and we lose one of the only two changes I have on the bench, two changes in terms of attacking areas, leaving us with just one change for the rest of the 90 minutes.
"I had to make Rashford play nearly 90 minutes when he clearly needs a bit of rest. Then, a very good referee, one of the most promising young referees, not just in England but in the world too, made a very bad decision that punished us.
"And then the game was about us trying, and missing, some important chances and always trying to create, they had one very good chance which David de Gea saved, but we kept trying with what we have at the moment. So, I think we deserved to win the match."
Romelu Lukaku expected to miss at least two matches
One of the bigger talking points of the match was Romelu Lukaku being stretchered off after just 10 minutes, following a nasty head collision with Saints defender Wesley Hoedt.
The Belgian striker has played out a mixed start to life at Manchester United, netting 10 league goals in his first 20 games but enduring lengthy droughts in between, and will certainly be missed during his absence.
His manager, who rightly looked incredibly concerned on the sideline, isn't clear of how bad the injury is, but expects his no. 9 to miss the next couple of games to kick-off 2018, at least:
“I don’t know [how bad the injury is]. I know that normally bad, bad news arrives immediately, and bad news didn’t arrive, but leaving the pitch the way he did is because there’s a problem, not just for today but at least for the next two matches, for sure.”