Video: Strong start helped us - Gray
Manager Martin Gray reckoned his side were deservedly rewarded for a strong first-half display against Curzon Ashton.
The Minstermen struck twice through leading goalscorer Jon Parkin and centre-back Daniel Parslow before Joe Guest claimed what proved only a consolation for the visitors following the interval.
"We started really well," Gray told BBC Radio York. "We knew we had to - and give the crowd something to enjoy. I thought the first-half performance was strong and we should have been 3-0 up at half-time. Jon Parkin has a great chance to make it three and I think that would have killed the game off."
Latest signing Gary Martin produced an impressive debut despite the former Middlesbrough striker having absolutely no game-time over recent months.
"He's got great quality and experience and played at a very high level," Gray continued. "His performance was very strong. He trained this week with a few niggles and was in doubt before the game.
"I know his background. He's a bit of a scally and I think he's got that toughness about him that was needed today."
Meanwhile, Gray doesn't believe the knock sustained by midfielder Adriano Moke to be anything too serious: "I think it was more of a kick from a misplaced pass but he'll be fine," he added.
Fellow midfielder Aidan Connolly is another with restricted involvement this season and also had to be replaced when noticeably tiring after the break.
"You can see the little fella hasn't had enough football over the last four or five months and is still trying to get up to the speed of things," Gray reflected. "For a good fifteen minutes he was very effective. You're just trying to get 75-80 minutes.
"I thought the fitness levels from the players today were outstanding. Four weeks ago we would have really struggled in that game. So a lot of credit to the players. We had great desire and a good shape off the ball and the substitutes made a difference when they came on as well.
"We still conceded a very soft goal and it's disappointing," he admitted. "Because that game should be 2-0, 3-0. They had one shot and scored all game.
"I thought Daniel Rowe had an outstanding debut having not played for the last two or three months. His decision making at the bottom of the diamond was very good."
Video Link: York City FC
Audio Link: BBC Radio York