But those sniping at the Norwegian will surely be a little quieter now after, in the space of four days, he masterminded victories over two of the most respected managers in the game, Jose Mourinho and Pep Guardiola.
After beating Champions League runners-up Tottenham Hotspur at Old Trafford, Solskjaer’s young side enjoyed a memorable 2-1 triumph over back-to-back champions and domestic treble winners Manchester City on their own patch on Saturday.
The United fans, who celebrated the victory at the end of the game with the manager and players, have not been the source of criticism of Solskjaer -- indeed the Norwegian has enjoyed strong backing from supporters who attend games at Old Trafford and those who travel away.
The noise tends to come from social media, talk-radio and pundits who are quick to judge from short-term results, which is a particularly inappropriate approach given the task Solskjaer has been given of creating a new, more youthful team, out of the mess he inherited from Mourinho almost a year ago.
Marcus Rashford, whose three goals and all-round performances in both this week’s wins, showed he has the talent and attitude to become a real long-term favourite at the club, summed up the situation well.
“It’s been an inconsistent start to the season, it’s a young team, and we’ve been trying to get the right fundamentals and the only way to get consistency is to go through these hard times,” he said.
“You have to stick with the manager and process. If we do that we’ve got something to be excited about in the future,”
The recent draws with Sheffield United and Aston Villa, were a reminder that much work remains to be done but the response means Solskjaer’s side are now fifth in the league, five points behind fourth-placed Chelsea.
United are the only team to have taken points off leaders Liverpool, with an October draw at Old Trafford, and they have beaten second-placed Leicester City, Chelsea and now City.
As Mourinho pointed out in midweek, United’s counter-attacking style is much better suited for games against the top teams and that was certainly the case at the Etihad.
Dan James and Anthony Martial provided pace and penetration down the flanks while Rashford continued to show his improvement in understanding the flow of attacks and his positioning within them.
In midfield Scott McTominay is now looking a Premier League quality defensive lynch-pin with Brazilian Fred flowering as a result of a regular run of starts. Jesse Lingard provides attacking options but showed another side of his game by effectively neutralising City’s deep midfielder Rodri.
Defensively, United showed a solidity that hasn’t always been there this season but they still needed outstanding saves from their Spanish keeper David De Gea to leave with the three points.
Solskjaer certainly feels that progress is being made.
“I’ve seen the improvement since I came, the boys have had to reshape the squad, change culture of the squad, the way we want to play,” he said.
It could, given the chances United created before and after their first-half goals, have been an even more emphatic result and the way they approached the game, with real self-belief, shows that something is working at the club’s Carrington training ground.
“I was so happy with the way we started the game, we created big chances, looked like we’d score. The intent was there to go forward, not about keeping it, slowing it down we go for the kill and should have been 3-0 or 4-0 up,” Solskjaer said.
“But you have to defend well, the way we prepared for this game, you follow this (City) team for three years, they’re so good and I am very pleased with how they dealt with everything, our boys.”