The win, which extended caretaker manager Solskjaer's unbeaten run in domestic football to 15 games, was much-needed after it appeared United would drop two potentially crucial points in the chase for a top-four finish and Champions League qualification.
New signings will be more hard to acquire if United fail to achieve Champions League qualification.
Asked if it was odd to do promotional work when still only interim boss, he said: "It'll be stranger to see yourself in the video if you're not here!"
When they look back on this game at the end of th season, the fans will do so still with a sense of excitement, of thrills and of how it was just like the good old days.
It's hard to compare them, but Edwin and Peter were never player of the year, David's meant so many points for us over the years and I would say he's the best goalkeeper in the world, Peter was at the time and Edwin at the time as well, I'm delighted with David and his personality is fantastic.
"We maybe found a better position for him than as a number six, more of an eight or 10".
"We spoke at half-time: get more urgency, get the ball in the box, and the strength of them [the fans] will suck the ball in. I don't want to speak about [that] for obvious reasons", he said.
"He's got high energy quality in his passing, crossing and shooting, so pleased for him, a goal and an assist, it's a nice day for him to remember".
"We'll do a scan [on Sunday] but we don't know until we've done the scan".
"Young kids at the start of their careers when they get criticism there's nothing better than seeing them grabbing their chance when they get it".
"I just said to him, "Get ready for the next one because you are going to take that one as well", the Red Devils boss said.
The report adds that the France worldwide "will hardly accept another season in the Europa League" like he did when they won the competition with Mourinho in 2016-17.
We were not far away from it and also after the 2-1 we did not stop attacking them and creating for us.
"We had some great play at times, 3-2 we did it the hard way".
"We came back and then one fantastic player decided this game with his unbelievable power and that's the end".
When Southampton went 1-0 up in the first half after a sensational goal from outside the box by Yan Valery, I was sure that the curse was going to continue. The second goal was offside, which isn't easy to stand.