Foyle told BBC Radio York: "I'm a great believer that if the league games have been put in, then they should stand.
"You can't keep chopping and changing the league programme."
Foyle said City's fixture pile-up is a "massive" worry, with the side facing two more league re-arrangements if they beat Barrow and reach the two-legged Trophy semi-final. Both ties would be scheduled for Saturdays.
It's probably the most hectic time I've ever known" York City boss Martin Foyle "It does hamper success and I see it being a little bit of a problem. Injury and form-wise things can turn very quickly over four or five games," he said.
Foyle added that he had not experienced this scale of fixture congestion during his years in the Football League.
"They seem to make sure everything's all right, they arrange the games properly.
"The League is a priority for us. The Trophy is a nice added sideshow for us, so we now need to concentrate on Barrow.
"It is a big competition. Maybe if it got down to the quarter-finals or semi-finals and they were Saturday fixtures I could understand that, but not (the) early (rounds).
"We're constantly trying to look at games as well, and at players for next year, it's probably the most hectic time I've ever known."