It was a frustrating afternoon for Blues, despite enjoying the vast majority of possession and chancesbcfc.com
It was one-way traffic for the most part in the PDL North, but Blues couldn't find that killer touch.
They hit the woodwork twice in the second-half, with Caolan Boyd-Munce being denied by a superb Sam Booth save.
And in added-time as Blues piled on the pressure, Connor Mahoney jinked to the side of two defenders inside the area and fired low, only to find Travis Johnson stationed on the line and able to clear.
Blues fielded a strong side, with David Davis playing the pivot role in a 4-1-3-2.
Kerim Mrabti played behind Isaac Vassell and Beryly Lubala, who Blues lost to a hamstring strain with 12 minutes to go.
Blues first sighter at goal came from Boyd-Munce, who had a strong game, who sent a sidefoot volley not too far wide.
Then when Mrabti teed up the Irishman on the edge of the box, he was unlucky to see a powerful goalbound attempt rebound off Joe Robbins.
Just before the interval and clipped cross by Remeao Hutton looked to be dropping awkwardly under the crossbar as Vassell went in, but 'keeper Booth did well to stay focused and somehow bat it safety.
In the second period Blues survived a strong shout by Crewe for a penalty but thereafter stepped things up and got their rotations and passing moving at a quicker rate.
More space began to be prised open and from a raid down the right by Hutton - one of several - his cross on the run bounced off the top of the crossbar and out of harm's way.
In the 55th minute, Lubala and Hutton combined to get the ball to Boyd-Munce, veering in-field onto his favoured left foot; he crafted the perfect angle and sent a curving shot towards the bottom corner, but Smith pulled off a stunning stop, getting fingertips to deflect it onto the post.
Again, Boyd-Munce's luck was out when this time Rio Adebisi blocked another of his fierce drives that was heading on target.
And as the attacks continued to build, following a corner Geraldo Bajrami headed down a second phase ball into the box and Mrabti crashed it at goal on the half-volley from close range but once more a red shirt was there to block.
Blues made a triple change in the 78th minute, with Josh Andrews and Odin Bailey going up front and Corey O'Keeffe coming on. Mahoney moved into Mrabti's number 10 role.
But Crewe continued to dig in and hold firm and despite urgent combinations in and around their area, as well as more direct balls and crosses, nothing would go Blues way.
It was symptomatic that, in the second minute of added-time, Mahoney latched onto a low pulled back cross by Hutton and had his drilled shot cleared off the line.
Blues: Trueman, Hutton, Dacres-Cogley, Davis, Bajrami, Redmond, Boyd-Munce, Mrabti (O'Keeffe 78), Vassell (Bailey 78), Lubala (Andrews 78), Mahoney. Subs not used: Jeacock, McCoy.