The Red Devils were 2-0 down after 20 minutes at St Mary's Stadium thanks to goals from Stuart Armstrong and Cedric Soares, but fought back before half-time thanks to goals from Romelu Lukaku and Ander Herrera .
United were forced into a makeshift 3-5-2 line-up, with Scott McTominay and Nemanja Matic in defence, with Paul Pogba and Herrera in central midfield alongside Marouane Fellaini.
Barring an impressive final 20 minutes in the first half, it was another lethargic display from Mourinho's men, with Pogba struggling in particular to make an impact as he lost the ball 25 times in the 90 minutes.
Mourinho felt a lack of "bite" allowed Armstrong to score Southampton's first and said his midfielders did not understand that "simplicity is genius" when trying to link the defence to the attack in a lifeless second half.
"We lost so many balls in midfield, so many balls in our transition to the last third that it was difficult to have that continuity," he told BT Sport .
2 - Marcus Rashford has provided two assists in a single game in all comps for Man Utd for just the second time in his career (also vs Crystal Palace in September 2017). Catalyst. pic.twitter.com/Lkw4zMo0X6— OptaJoe (@OptaJoe) December 1, 2018
"We did so well in the last 15, 20 minutes of the first half, we chose to connect to the attacking players by transporting the ball, the right choice of pass, accelerating the game, but in the second half we went back to that dynamic.
"The players don't understand that simplicity is genius. They keep, keep going to complicated football. But [there was] good spirit, good fight, a great example of players fighting until the limit. I would say, as positive examples, Marcus Rashford, Phil Jones, many others showing that respect for the shirt.
"The second goal was a direct free-kick and the first was because we didn't press enough the ball, which is something we do wrong. It doesn't matter the system we play, it has to do with the characteristics of the players.
"We don't have many - I hope people understand what I mean - we don't have many mad dogs, who bite the ball all the time. Scott and Matic did a very positive job for two midfield players and Phil Jones leads that group of three in a way we are totally in control.
"What we needed to improve in this game is simplicity in midfield. By losing so many balls in midfield, we broke that dynamic that normally leads to goals."
Mourinho's reaction to a miss from Marcus Rashford against Young Boys was heavily scrutinised, but the United manager was full of praise for the forward, who set up both of United's goals with positive runs, even though he failed to score.
"I'm pleased with him even without that [goal] because his work rate was amazing," he said. "He was doing things other people have to do, defending on the sides, trying to give solutions in midfield to connect the game with attacking payers. He tried to do everything.
"The only thing missing was a goal, but I can only praise him, like I always do with players with such a desire and respect for the shirt."