Crewe took a first-half lead through on-loan QPR player Tom Hitchcock, who 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 Taylor, who rushed on to a long ball before smashing into the net from inside the box.
"When you've come away from home and you're a goal down, to come back and take away a point is reasonable," Turner said.
"But I just felt that we had some good opportunities second half, good positions, a couple of good opportunities, that we should have done better with.
"So it's a little bit mixed feelings, but I think we've got to be relatively pleased with a point away from home coming back from one-down.
"We didn't really deal with their forward players. There was a lot of balls that we had difficulty with, but as we grew into it, we got better.
"It was a difficult surface and on the odd occasion we did pass it, we looked a threat.
"It was a cracking finish from Jon Taylor, but he can make those runs.
"He's bright enough to pick out the right time to go and he's bright enough to finish them off. I want to see more of that."
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.