The left-back was replaced by Axel Tuanzebe in the 67th minute having picked up a knock. Following an assessment, the club have now confirmed that he faces four weeks on the sidelines to recover.
Solskjaer had hammered the authorities for the scheduling of the game which saw United playing at 12:30pm UK on Saturday lunchtime despite only arriving back from their Champions League clash in Turkey at 4am on Thursday morning.
The United boss was furious following his side’s win at Goodison Park and pointed the finger at those in charge of scheduling for not thinking about the welfare of his players.
“They set up the boys to fail,” Solskjaer said. “We have got Luke Shaw injured because we have played loads of games this season already, been to Turkey on Wednesday, got back at 4am on Thursday and we are playing a lunchtime kick-off on Saturday.
“It is an absolute shambles and I cannot praise the boys enough for the character they have shown. That is all I want to talk about. Those boys deserve better than being thrown out here to fail today. The authorities set us up to fail.”
United will have Alex Telles available after the international break. The summer signing has missed the last five fixtures, having made his debut against Paris Saint-Germain, as he tested positive for Covid-19 and was forced to self-isolate for two weeks.
The England national team confirmed that they are expecting the striker to link up with them on Thursday following additional tests on his injury – but there has yet to be confirmation on whether or not he will be available.
United face West Brom at Old Trafford in their next game in the Premier League and Solskjaer will also be keeping a close eye on Victor Lindelof, who the manager confirmed still had a slight back problem despite featuring in the 3-1 win over Everton.
The Swede is expected on international duty this week, although he won’t be meeting up with his team-mates in Denmark due to current Covid-19 quarantine restrictions. He is expected to fly to Stockholm to meet up with the group later in the week.