Well, if you actually watch our games, you could see we are always building possession from the back with Lindelöf and Maguire, they find the right passes to break the lines and to play fast through. They play in the little spaces with quick passes and often forward. We also keep the ball a lot more than before with Jose. We use our fullbacks way more and they participate on the building part and last movement (crosses, key passes through the lines).
But, McTominay and Pogba are injured all the time, Lingard and Andreas are ineffective creatively and our forwards have been out injured too or out of form. You also can see that we don't have any viable options on the right flank, James being unrecognizable for few weeks now. And now Rashford is out, we have a problem on the left wing. Our squad was already paper thin but with all theses injuries and out of form players, it's complicated for any manager, even the better. And I know there are a lot of better managers than Solskjaer but he'll give all he have for our club and will put the culture first, the one why we felt in love with Manchester United.
So no, our playing style is not counter attacking, surely not. And yes, Ole lacks a lot of things to implement the kind of football he wants his team to play. Once we have all our players back and 2-3 additions in the summer (DM, RW, CAM), I'm sure we'll more progress than we actually see.