Jennison Myrie-Williams' last-gasp strike handed the visitors all three points as he snuck in at the back post to tap home a cross that ran right along the Alex six-yard box.
The defeat extends Crewe's winless run to seven matches and piled more pressure on boss Davis as his side sunk deeper into the Sky Bet League One relegation zone.
But the manager believed his side deserved more from the game.
"We lost the game and I'm obviously disappointed to not win in the end," Davis said.
"We started very well, got a good early goal and weren't able to capitalise on it.
"I thought we had some good periods and dominated the first 35 minutes.
"At 1-1, I thought if we could have nicked another goal, it might have been different for us.
"Second half, both teams are trying to break each other down and there wasn't a lot of chances, the game was quite even, and it's just a little one-two that's got in behind us.
"But I was pleased with the team. We were a team, which we haven't been in the past.
"We worked very hard, everyone worked hard for each other and we gave everything we had.
"it gives me a lot of hope, performances like that, when the players have tried and worn their hearts on their sleeves like they did."
A tense start saw Crewe have the best of the chances as they pushed for the first goal in front of a bumper Gresty Road crowd.
And they took a deserved lead through a stunning strike after 34 minutes from Manchester City loanee George Evans.
It was a goal of the season contender from the teenager, who received the ball 25 yards from goal and only needed one touch to send home a stunning side-footed volley that dipped perfectly over Vale keeper Chris Neal and into the top corner.
Alex had earlier come close to breaking the deadlock after 19 minutes, with Evans again involved as he curled against the post from 22 yards.
As full-time loomed Myrie-Williams popped up at the back post to easily net and send an army of over 2,000 Vale fans into jubilation.
- Sports & Recreation