Two of the five defeats since have come against Barcelona but Solskjaer clearly has a rebuilding job ahead of him, and admitted as much after Tuesday night's 3-0 loss at the Nou Camp.
'This Barcelona team are the level we have to aspire to.
United is now on its worst run of results this season and some of Solskjaer's selections are being scrutinized - for example, left back Luke Shaw playing as a left-sided center back in the first leg against Barcelona and center back Victor Lindelof as a right back in the second leg. If the first 15 minutes had gone our way, it would have been a different game.
"We have a great team and we have Leo..."
He said: "They played very well".
United began positively with Rashford prodding a shot against the bar inside one minute, but they cultivated their own downfall within the space of four minutes.
A wonderful run as a caretaker, capped by coming from 2-0 down to beat Paris Saint-Germain 3-1 in the French capital to progress on away goals in the last 16, made Solskjaer's case for the job on a permanent basis hard to ignore. Rivaldo is confident Coutinho can get the fans onside by contributing more goals and rising to the occasion when Messi and Luis Suarez fail to do so.
It was a miserable return to the Nou Camp for United manager Ole Gunnar Solskjaer, who scored the victor 20 years ago as the club beat Bayern Munich to win the Champions League and clinch the Treble.
This is what I meant when I said that there was such a cloud over United that all Ole had to do was to come in and change the environment. "The quality of finishing was outstanding", the former striker said in his post-match press conference.
Just four minutes later, Messi effectively clinched Barca's return to the semi-finals for the first time since 2015 with a helping hand from United keeper De Gea, whose woeful attempted save failed to stop the Argentine's weak shot slip under his body.
"We can not start like this in any Champions League game", Messi told reporters.
"Messi is an exceptional talent, him and Cristiano (Ronaldo) have been the best players in the world in the last decade".
"He is a player that can get 25 goals per season and can score in important matches".
"The attitude was right, we were fighting against a good team and good players out there".