Davis' side remain in deep trouble in Sky Bet League One despite extending their unbeaten run to three games.
But it could have been so much better for Crewe had they not relinquished a first-half lead handed to them by on-loan QPR player Tom Hitchcock.
The striker netted his second goal in as many games when he stooped low to nod home Chuks Aneke's knock down from Mesca Banga's clipped cross for a wonderful team goal.
But Alex failed to build on their lead, and in the 55th minute Shrewsbury grabbed a deserved equaliser through Jon Taylor, who rushed on to a long ball before smashing into the net from inside the box.
Although he thought a point was a fair result, Davis was unhappy at the manner in which his side conceded.
"I was disappointed with the goal," he said.
"It was just a long punt down the middle, and I think Mark Ellis, for whatever reason, ducked under it, could have headed it.
"He'd made a couple of runs in the first half, which at half-time I made them aware of because he was making them across the centre-halves.
"Then I thought Ben Garratt could have stopped it - it just went over his head. I've questioned him for that.
"So I'm looking at four mistakes and funnily enough, James Collins said 'if we're going to concede, it's going to be a mistake, followed by a mistake, followed by mistake'.
"Low and behold, that's exactly what happened.
"In the end it was probably fair."
It was a stop-start game, with a long delay incurred when Crewe's Adam Dugdale was stretchered off after just eight minutes.
The Alex defender required treatment from eight medical staff after injuring himself during a typically wholehearted tackle that saw Luke Summerfield land on awkwardly on top of him.
Town should have nicked it late on, but a lazy prod from Tom Eaves rolled straight to Garratt when the striker was one-on-one in injury time.