Zaha began his spell with the Bluebirds brightly, but he has been left out of their last two games by Solskjaer.
But the Cardiff boss insists that Zaha still features heavily in his plans.
"The original plan was to play Wilf on Saturday, but I decided instead to go with Fraizer Campbell who I thought might only last 60 minutes, but instead gave us everything he had," he said.
"Of course Zaha has a big role to play, or I would not have brought him to the club."
None of Cardiff's strikers have scored since the start of February when Kenwyne Jones bagged the winner against Norwich, and Solskjaer insists he is working them hard.
"I have been a striker myself and I know what they think and what they feel, and what they want from their training," he said.
"It is about practising - I have started putting crosses in for them myself, don't worry about that.
"I understand what kind of situations will benefit them, and that is what we are doing. They will practise what they do in a game.
"At times we take them to work separately - you nurture them and give them some TLC because as a striker you want that.
"It can be tough when you are not scoring, but then one day you will score off your backside and you think you are the best in the world again.
"That is the confidence you need as a striker. It is a fine line between missing and scoring. Most of the goals will be scored from one touch."