Taddy made three changes to the team that saw off Mossley on Saturday with Conor Sellars & Rob Youhill recalled plus, a first start for Charlie Binns in midfield.
The best chance of the game came after just eleven minutes, and it fell to The Brewers.
Conor Sellars placed a perfect diagonal ball over the top of the full-back to the advancing Steve Jeff who closed in on goal and lashed agonisingly wide of the near post.
A trio of minutes later and Taddy created what was to be their second best chance of the afternoon.
Sellars' deep cross was headed up and out to the edge of the box where Binns stood and volleyed at goal first-time which dipped just an inch over the mark.
The league leaders had a few efforts at goal well blocked by the Brewers' back line in the opening stages.
James Walshaw had the first real sighting at goal for the visitors as he peeled off his man but could only head into the ground making it a simple pick-up for Ingham.
The former Harrogate Town frontman did find the net moments later but was met by the linesman's flag floating high in the air.
McKibbin in the Celts goal was to be tested right on the half-time whistle. Conor Sellars clipped a free-kick up and over the wall to which the Farsley stopped got across well to push away.
Taddy had the better chances at goal in the first half but the visitors responded well and began the second half on the front foot, albeit without creating any opportunities.
It was a battle of two very well organised sides as defences were certainly on top.
The Celts put in a few good crosses into the box but the likes of Andy Milne, Gregg Anderson, Josh Barrett, Steve Jeff and Jason Mycoe were solid at the back once again.
Tom Corner's strike from the edge of the area was routine for McKibbin.
With time running down, The Brewers were ever so slightly sniffing for that elusive winning goal. They sensed they had a chance when McKibbin dropped a corner at Corner's feet but with his back to goal the shot was improbable.
After playing the ball back out to Sellars, who then produced his wizardry to beat his man and fire goal wards but the scuffed effort was this time gladly picked up by the goalkeeper.
With stoppage time approaching, Taddy had a good shout for a penalty as James Knowles quite literally caught a ride on the back of Tom Corner clambering all over the towering forward.
The referee Elliott Howard looked at the incident but decided not to award anything and that wrapped up proceedings.
All in all it was two teams who cancelled each other out.
A good point for The Brewers who couldn't quite find a way through Farsley's back line who still wait to concede their first goal of the season.
Team: Ingham, Barrett, Jeff, Milne, Anderson (Morgan 90), Mycoe, Youhill (Ibrahimi 71), Beadle (c) (Baker 55), Corner, Binns, Sellars
Unused: Shepherd & Parker
ATT: 510