The Red Devils were put to the sword thanks to Andros Townsend and Wilfried Zaha’s second half brace.
The Manchester-based club have suffered their first league defeat in 15 Premier League games stretching back to January when they lost 2-0 to Burnley.
Solskjaer believes Manchester United were second best in all departments as the Eagles secured their second successive win in the Premier League.
The Norwegian coach admitted his men performed like a team playing in a pre-season game.
"It's not bits and pieces that decided the game, that's for sure. We didn't deserve to get anything from the game,” Solskjaer told Sky Sports.
“We started badly and slowly, we looked like a team early on in their preparation in pre-season.
"You could see that they came flying out of the traps. You could see the difference between their prep with four friendlies and this is their third game this season whereas this is only our first game. We had one friendly last week but I think it showed. We were way short.
"You could see the physicality here this evening. They were sharper than us, they were stronger than us and we've got to catch up quickly. We can't wait to have a normal pre-season and our next game is already on Tuesday."
Next up for Manchester United is a visit to the Kenilworth Road to face Luton in the English League Cup.
