"We know what we're capable of", he said.
Centre back Chris Smalling picked up his dry cleaning while fellow defender Diogo Dalot, now enjoying a run in the side, went for a fresh trim.
Solskjaer famously scored the stoppage-time victor as United completed a late turnaround against Bayern Munich in the 1999 Champions League final at Camp Nou.
Romelu Lukaku was the match-winner in both of those encounters, scoring four goals across the pair of fixtures.
But this was to be United's day and Lukaku struck home two minutes from time in a 3-2 win that propels Solskjaer's side back into the top four.
Lukaku cut a relaxed figure on Monday afternoon as he strolled through town in jeans and a khaki bomber jacket. We have to do it away from home, but we have eight straight wins away from home.
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This win over Southampton made it 10 victories in 12 league matches under Solskjaer and lifted United above Arsenal - and to within three points of third-place Tottenham. That shows that they can compete with the biggest teams in the English Premier League, and Manchester United will be well aware of entering this contest that they aren't to be taken lightly.
The Belgium worldwide had stepped up to take the injury-time penalty to clinch his debut hat-trick but watched on as Pogba saw his effort saved by Angus Gunn.
After a lacklustre first-half display, United were now in an irrepressible mood and took the lead just six minutes later through Lukaku.
Romelu Lukaku was the hero for Manchester United on Saturday at Old Trafford as he scored two goals that not only saved the Red Devils from the jaw of defeat but handed them crucial three points against Southampton.
With a 2-0 win over fellow bottom club, Fulham helping to further boost their survival chances, Saints boss Ralph Hasenhuttl may be loathed to make any changes.
"I think the badge speaks for itself when we talk about comebacks, desire and attitude, and for us it was just another game that we gave everything in".
Mourinho won the EFL Cup and Europa League at Old Trafford, and guided the team back into the Champions League, leaving the 56-year-old to defend his record at the helm, and his interaction with the squad. We spoke about it at half-time and said get the ball in the box and play more forward because the Stretford End will suck it in for you.