Rashford burst onto the scene with four goals in his first two appearances, arguably giving Van Gaal a second wind as rumours he was to be sacked grew.
The Dutch manager gained further breathing space with a 1-0 win over Watford midweek, making it four consecutive United victories.
"I have read that Rashford is saving me. No, no," Van Gaal fired in his press conference.
"Rashford has got his chance thanks to my policy, and the club's, of course.
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"The same thing applies for Cameron Borthwick-Jackson, Guillermo Varela, and a lot of the other young players.
"That is why we didn't invest in January. Our policy is to have a small squad to allow space for young players."
United take on West Brom on Sunday, a game which could lift Van Gaal's men into a Champions League spot should other results go their way.