The Alex took an early lead when Tom Hitchcock slotted home Chuks Aneke's throughball but City turned the game on its head as Franck Moussa scored just before half-time and Callum Wilson then converted a spot-kick.
But Chris Maguire and Jordan Clarke got themselves in a mess in their own half and allowed Hitchcock to rob the ball and return the favour to Aneke, who scored from just inside the box.
It was the first time this season that Crewe have come from behind to earn a draw.
Pressley said: "They were horrendous conditions but we were so in control of the game when we got to 2-1 and it looked like there would only be one winner.
"We gave away a really disappointing goal that allowed them back in the game. Both goals were disappointing for me because at no time were we ever in danger. We look like a team that isn't going to concede goals but we are conceding goals purely on errors.
"We look a good unit and if we cut those errors out we will be an excellent side.
"I thought we gave a terrific performance. I asked for the pressing game which we saw, I asked for controlled possession which we gave and I asked for counter-attack when it was on, which I saw.
"Our choices were good and I thought it was a mature performance in the conditions.
"We got the right response from conceding the first goal and I thought we finished the first half in a really aggressive manner. I was pleased at half-time with the performance and I was pleased at full-time with the performance, I'm just disappointed we didn't get the result."