Neither side created many chances, but Brig dominated possession, dictating the tempo of the match throughout but not using it to their advantage.
The first real chance of the match came on 24 minutes when Jamie Milligan’s cross deep from the left hand side found Brig’s Adam Dodd, but his tame header was just wide of the goal.
Tadcaster did give Brig a scare at the end of the first half when a shot from 25 yards from their impressive number nine, Connor Sellars, sailed just wide of Steven James’ right hand post.
With the first half failing to wow the crowd of 162, the second half was much the same, with neither side really troubling their respective goalkeepers.
The best, and frankly only real chance for Brig after the break, came on 66 minutes when Macauley Wilson won back possession following a corner clearance.
His darting run at the Albion defence created space for a shot at the corner of the 18 yard box, but his curling effort was just wide of the far post.
Meanwhile, in the FA Cup, Lancaster City produced a battling performance but were beaten narrowly by Nationa League North outfit Kidderminster Harriers 3-2 at Giant Axe.
Andre Brown opened the scoring for the visitors, only for Jordan Connerton to level matters.
Billy Akrigg smashed home a worldy from 35 yards to give City the lead but Kidderminster hit back in the second half to win through Brown and Tyrell Waite.