Mason Greenwood had equalised for United against the run of play but in truth they rarely threatened the Foxes.
It means United now have the Europa League as their only chance of silverware this season.
Solskjaer believes his players are exhausted and that was the reason they struggled to create against an impressive Leicester side.
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“We played every three days and been on a great run. It just caught up with us, all the games and travels. Thursday night in Milan was a big night and took a lot of out of us physically. We didn’t have the extra zip, authority and confidence today.
“We tried to get on the front foot and start well because sometimes you can get that adrenaline boost and confidence if you get a goal and that can carry you over the line.
“We’ve got too many players that have played too many games and too many that haven’t really had much football, Anthony Martial, Donny van de Beek, Paul Pogba and others are trying to get in who haven’t had enough football.
“We didn’t have enough against a tough team.”
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Some United fans were surprised when the likes of Bruno Fernandes, Edinson Cavani and Scott McTominay were only on the bench.
Solskjaer explained: “I would’ve done the same again, the changes were necessary to do.
“We knew Paul [Pogba] wouldn’t last more than an hour and I don’t think I would do anything differently. What goes on behind the scenes isn’t always known.”