The top four teams at the end of the season qualify for Europe's elite club competition, with United now fifth, a point and a place below Arsenal and two points above Chelsea, who host third-placed Tottenham Hotspur on Wednesday.
"Play well when he gets a chance, keep on training as he does, keep working", Solskjaer said when asked what the Brazil worldwide needs to do.
Coming up against his former club again as well as a former manager, Zaha will be hoping to influence the game in favour of an in-form Crystal Palace side that has won four and drawn two of their last six games in all competitions.
Jeffrey Schlupp nearly produced an immediate response when he glanced wide from close range but, if they remained in contention for a point, further poor defending undermined them as Lukaku extended United's lead in the second half.
"They've been very, very good".
"We came for a win, of course we did, but we definitely didn't want to get beat and we wanted to take something away, and we have managed that".
"These big teams are showing us respect but maybe we need to start respecting ourselves". They are averaging 10 more sprints per match under Solskjaer than under Jose Mourinho.
Here's the Man Utd XI that could start on Wednesday against Palace.
Whereas Sanchez drifted inside from the left, Dalot never moved from the right flank, which meant Palace never had space to break into down that side.
A dip in form - one that some argue signals a capitulation - culminated with a point at one of the most historically hard grounds to play at, against a Manchester United side who had won every game but one since losing at Anfield back in December.
"It shouldn't be defined by one game but to beat Chelsea, Tottenham, Arsenal and then Liverpool it would nearly make it impossible for him not to get the job".
At Selhurst Park however, Shaw showed off the other part of his game, grabbing an assist in a 3-1 win. The interim manager did claim, however, that the intensity of his team needed improving and injuries are a by-product.
Asked if the increased running he demands has brought on the muscle injuries, Solskjaer said: "It's probably linked, yes, because when do you make that change?" Do you wait until pre-season and think you will change results by just not asking them to run?
"You have seen what I have chosen", he added. "So often when you play teams of this quality, they find a way of picking you off".