Goals from Junior Brown and a late strike from Steven Gillespie were enough to seal three points and keep the Cod Army in the promotion places.
But Mellon admitted: "York never seem to disappoint us. We knew it was always going to be a very difficult game.
"They came out of the traps very well but we defended well and my goalkeeper has made a couple of great saves.
"You expect that when you come to York though, and you would expect that if you came to Fleetwood. We rode that out and then scored a fantastic goal.
"I'm delighted with the overall performance from my team because it's a hard place to come. We hit the post and we had a couple of one-on-ones which we may have done better with but I can't complain with the result here at all."