When asked if there were any injuries at Everton, Solskjaer told MUTV: "Yes".
A 2-1 defeat to Istanbul Basaksehir in a Champions League group stage clash in Turkey on Wednesday piled more pressure on Solskjaer, who refused to be drawn on speculation over his future post-match.
The current United boss has overseen a shaky start to the new season for United, with his side now 15th in the table having won just two of their opening six Premier League fixtures.
"Our players were set up to fail today with the schedule", he added. What sense is there for us to play on a Saturday when we could play on the Sunday and there is an global break afterwards? It's how you deal with that setback and from what I've seen from the boys, they've been very focused.
He has been so good for United that they went unbeaten last season after the league resumed after the Coronavirus break.
The Portuguese powered a header from a Luke Shaw cross past a flailing Jordan Pickford and scored again when an intended cross for Marcus Rashford was missed by the England worldwide and the ball crept in off the far post.
If the Red Devils were to turn to Nagelsmann they would be getting one of the most prominent and exciting managers in world football, with the 33-year-old attracting attention for his success in the Bundesliga at both Hoffenheim and now Leipzig, whom he took to the Champions League semi-finals last season.
We also saw a somewhat shocking result at Selhurst Park as Crystal Palace ran out 4-1 winners over Leeds United, and while that isn't necessarily a sign that the Yorkshire club are in trouble, it does showcase the struggles they could have if they continue to push forward as strongly as they have been thus far.
It was Timo Werner's turn just three minutes later as he scored Chelsea's fourth goal of the afternoon to make it four consecutive wins for Frank Lampard and his players across the Premier League and Champions League.
Elsewhere this weekend, if Liverpool drop points against City, then Leicester, who host Wolves, or Tottenham, who travel to West Bromwich Albion, could seize first place.
Chelsea had a poor start at Stamford Bridge but came from behind to beat bottom club Sheffield United in superb fashion.
Everton, meanwhile, have lost three straight games after having started the campaign with four wins in a row.
