Goals from Marcus Rashford and Anthony Martial in each half were enough to beat a spirited Palace team as United mount pressure on Chelsea and Leicester City.
Solskjaer insisted his side must have belief and confidence to win their last two matches in order to stand a chance of qualifying for next season’s Champions League.
“We have two games we need to win. The players should be confident, trust themselves and trust the way they play,” the Norwegian tactician said after the Red Devils victory in South London.
Manchester United were lucky not to have been pegged back by the hosts on the 55th minute mark when Jordan Ayew’s effort was ruled out by VAR.
The former Cardiff City and Molde FK boss admitted he knew Palace would be tough and insists they were lucky VAR came to their rescue.
“We know that the other teams will do their bit but we have to concentrate on ourselves, we took some time to get going today and Palace were on the front foot pressing us,” Solskjaer added.
“When the play and interchange and movement came, it was nice to watch.”
"Their disallowed goal looked tight and you are hoping it is offside, we were lucky there.
"We need to be more clinical in finding that type of play, when they do they are good to watch. They are so good, strong and technical and put the defenders on the back foot.
Manchester United now turn their attention to the FA Cup semi-final as they prepare to face Chelsea at Wembley on Sunday.
