The Minstermen bossed the first half but failed to take advantage with Matty Blair and Michael Potts failing to convert good chances to hand their side an early advantage.
The home side came into the game as the second half progressed and could have snatched the lead with ten minutes remaining, Steven Gillespie's shot cannoning wide off the boots of City keeper Michael Ingham.
"I would have said before the game a draw would be points lost but after that I would say we gained two," Alexander said.
"We didn't play well enough to win the game. York were the superior team in the first half.
"Second half we got at them a little more but I'm not going to lie and say I thought we should have three points because I don't think we should.
"We haven't asked them to do anything different from the last three games. We just lacked aggression and energy.
"It doesn't matter what tactics or formation you play if you lack that you're not going to make anything of the game. There are two positives to take, we've got a points and we've got a clean sheet."