That, ironically, came from the harshest criticism of all.
Roy Keane’s well-publicised analysis was naturally put to Solskjaer, specifically the use of the word “bluffers”. The Manchester United boss had evidently heard it, though, because he tried to suppress a smile as the question was being asked.
The Norwegian then deflected a little bit as he deferred to his friendship with Keane, and how much the former captain cares about the club, but did end with a hard point of his own.
“That's my job, to make sure we have the right characters.”
Keane’s specific comments on Paul Pogba weren’t put to Solskjaer, but that is now one of the biggest questions of all - whether the French star is one of the right characters.
Because while anyone can name the many players the United boss would want to get rid of, it’s a lot more difficult to say what should be done with the French star - and what he is supposed to be doing right now.
This was another bad individual performance, from the player supposed to be the best on the United team.
Hanging over all of this is the fact he remains the one star they want to keep above anyone else. A significant part of this is because of his commercial value outside the field, but it is getting to the point where you have to wonder if it’s worth it.
Forget all the irrelevancies like his social media use, or his haircuts. They don’t affect performance in the slightest, no matter what more old-fashioned pundits - perplexed by something outside their own culture - might say.
A lot of that criticism is pure bulls***.
But where there is no bulls***, to paraphrase Martin Scorsese’s Mean Streets, is the pitch.
And right now, the reality for Pogba is galling. Even worse for him, he is proving Jose Mourinho so right.
This defeat against Manchester City felt so definitive in that regard.
Pogba, more than any other player because of his role, came to so fully represent United’s ponderousness against the champions’ sharpness.
He actually came to represent a tactical problem, too.
Because even when United’s stretched and limited backline were defending manfully in the first half, they were coming under increasing pressure because those in front weren’t using it properly. Pogba, in his role as the main creator, just couldn’t get the ball to Jesse Lingard and Marcus Rashford quick enough.
He was taking four touches where City’s midfielders only required one.
The gap in application was startling.
It might of course be argued Pogba would do so much better with better players around him. He might well revel under Pep Guardiola, who would surely bring so much more out of him in the way Kevin De Bruyne has spoken about.
Even allowing for all that, though, his performance reflects a recurring problem. Pogba is just too often too casual.
He is all the more frustrating because he doesn’t seem to be fully focusing his abundant talent. You can see what’s there but don’t often enough see its effects.
Compare that to City’s mettle. Pep Guardiola’s side showed the perseverance and nerve here you would have seen from great Sir Alex Ferguson sides of the past - but not so far from Pogba.
And it begs the question: why would City have wanted him when Mina Raiola was hawking him around at this stage last year? He currently looks way off the kind of resilience City showed at Old Trafford, and just at the point when his own team need him to show it most.
Why, at the same time, are Real Madrid so set on him? Multiple sources - from Manchester to Paris to Madrid - now say Pogba’s representatives have been in deep discussion with the Spanish club, to the point they could easily agree personal terms.
But, on the evidence of this, why? And why wouldn't United sell? Why not insist on a swap for stars who have shown they can do it, like Raphael Varane, or Toni Kroos?
Pogba still hasn’t justified his price. Or, more pointedly, he still hasn’t justified the faith in him that such a price represents. He still hasn’t shown he is worth building a team around. He doesn’t give anywhere near as much as his status denotes. Other than when given specific tactical instructions in a limited role as with France, he just allows too many games to pass him by.
His very signing, and the rationale behind it, thereby remains one big reason why City have so passed United by.
Pogba - remarkable as it sounds, given his situation and how much United do want to keep him - is one of those that needs to show Solskjaer, and everyone else, he is the right character.
We haven’t seen anywhere near enough yet.
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