In the end, the Norwegian was left discussing a failing that has been at the forefront of his mind in recent weeks.
At Old Trafford, it was Chelsea who finished much the stronger during the 1-1 draw between the two sides.
After a decent first-half performance in which his side had taken the lead through a brilliantly-worked Juan Mata goal – only to be pegged back by Marcos Alonso after David de Gea added to his growing catalogue of recent errors – United were unable to press on in the second period.
Solskjaer has been lamenting his side’s lack of fitness and work-rate in recent weeks; after the 4-0 thumping at Everton , he apologised to supporters for his side’s non-performance.
And on Sunday, there was no getting away from it.
Because while his side knew that they needed to win, and mentally may well have wanted to push for the three points late in the day, physically they couldn’t manage it.
In the first half, United pressed, set traps, got in the faces of Maurizio Sarri’s men with intensity and intelligence. They played on the front foot and that’s how Solskjaer, long term, wants his side to play.
In the second 45′ they got nowhere near that level of performance and it was Chelsea who looked more likely winners prior to the final whistle.
Romelu Lukaku, who played the full 90 minutes, looked gassed even before the break. Marcus Rashford went off injured having played, again, in fits and starts.
Scott McTominay replaced Mata, who cannot last 90 minutes, simply to add legs.
“We were tired towards the end of the game,” Solskjaer said. “That’s for sure. We’ve addressed that issue before, we have just got to take one step at a time.
“And there were periods today you feel when Scotty comes on we get those legs again, legs going, and we depend on everyone being fresh and fit.
“[First half] We looked really, really sharp, really good, and for whatever reason, in the second-half we didn’t come out and play.”
That is something that Solskjaer must fix and is also an issue for which he will need help from executive vice-chairman Ed Woodward to fully solve this summer.
Solskjaer wants to bring in players with pace – ala Jadon Sancho – who can excite fans and is also keen to bring in greater quality, of course.
But he is also equally determined to bring in players without injury baggage, to improve the fitness of those he currently has, and to rid the club of those who simply can’t do what he demands.
Solskjaer aspires his United side to be masters of late goals once again, just like during his playing days under Sir Alex Ferguson.
It wasn’t coincidence. It was because they wore down opponents throughout and were then fit enough to take advantage late in the day.
Now, they’re nowhere near, something Solskjaer is all too aware of and will be looking to rectify during pre-season.
After the Everton loss, Solskjaer declared: “We know our fitness is nowhere near good enough. I’ve said it before, I can’t wait to get a pre-season done.”
As he arrived at Carrington on Monday to go through yesterday’s encounter, Solskjaer will have almost certainly been having similar thoughts.
Now that their Champions League hopes are all but over, summer cannot come quickly enough.