The visitors had the better of the chances and nearly won the game late on with both Steve Howard and Andy Monkhouse seeing headers cleared off the line with the clock ticking down.
Cooper was pleased with the effort shown by his players and he is now hoping his side can build on their first point.
"We spoke before the game about when you're away from home in any league you have a little checklist of things to do and having watched York previously I have to say they've ticked everything," he explained.
"I was pleased with that aspect and I also had a checklist for when we were in possession and I think there are things we can improve on. I've said to the lads as long as you give me that I can't ask for anymore.
"Was there only one team who looked threatening to winning the game? I think so, but credit to York as they've defended their box very well. We've created one or two chances and I've said to the young forwards they've got to learn to gamble more in the area.
"On the whole, to get our first point of the season I'm very pleased."