The Minstermen went down 1-0 at relegation-threatened Gainsborough Trinity - their third defeat in a row.
The result has put their National League North play-off spot in major doubt with York now sitting a point outside the top seven.
Crucially, Chorley and Spennymoor have games in hand meaning York’s destiny is no longer in their own hands.
Gray admits York have not been good enough recently but says he is committed to bringing the good times back.
"It's been the toughest day since we have come into the club," he told York’s website. "When things aren't going well, the players probably feel a lot of pressure on their shoulders.
“They understand the total pressure from the fans. The expectations of the people at the club are massive and the expectations of what players have to deliver.
"I understand the total disappointment from everybody. I want to turn it around. I hope I am given the opportunity to do that because I am working very, very hard.
"I apologise to the York fans. It's been very, very difficult for them. But we have got to remain focused. We have still got a chance. It's getting more difficult. I will not go hiding and I hope the players do not go hiding.”
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