The Bees will have to settle for a replay after a second half Tyler Walton strike cancelled out Simeon Akinola's early opener at the Citadel Stadium.
HOW IT HAPPENED
The first opening fell the way of the hosts as Callum Reynolds did brilliantly to head behind a dangerous delivery from an early corner kick.
The Bees started on the front foot and looked to exploit the space in behind the Celtic's backline, however, Mason-Clark was adjudged offside on two occasions in the opening stages.
On the 10th minute, the Bees took the lead as the ball fell to Simeon Akinola on the edge of the box and he delightfully curled it into the top corner. He left 'keeper Scott Wynne with no chance and delivered the perfect start for his side.
Two minutes later Mason-Clark took on the Farsley defence before firing an effort just wide of the left-hand post.
Cheye Alexander was next to go close as he fired high from six yards out following good work on the left from David Tutonda. On a difficult pitch, Darren Currie's side started the better and dominated the opening 25 minutes at the Citadel.
Up the other end, the hosts looked to bring themselves back into the tie and Loach had to do well to turn around a Jimmy Spencer strike. Six back to back corners followed and the Bees had to defend resolutely from several dangerous deliveries, however, the lead was maintained following the wave of Farsley Celtic pressure.
The Bees showed great grit in tough conditions to defend against a physical and gritty Celtic side who were looking to use those conditions to their advantage.
As added time approached the hosts produced their best chance of the half as Dave Syers flicked a header just over the crossbar following a dangerous cross from danger man Will Hayhurst. Although, straight up the other end Mason-Clark stung the palms of Wynne as the half time whistle blew.
Seven minutes into the second half and the hosts levelled as Tyler Walton slotted home as the ball fell kindly to him inside the six-yard box.
Currie responded immediately by introducing Mauro Vilhete and the lead was almost restored immediately as James Dunne saw a powerful effort well saved by Wynne. From the resulting corner, Elito looked to have curled all the way in but it was stabbed clear from the goal-line.
On the hour mark, Akinola tried an audacious effort from 30 yards out that narrowly went wide of the post, it was a good effort and it was another sign of the Bees trying to stamp their authority on the tie.
The Bees were let off with 63 minutes on the clock as Spencer was allowed a free shot on goal from the edge of the box, he should have done better as he fired over Loach's goal.
The conditions certainly didn't help proceedings and both sides struggled on a boggy, bobbly pitch. Celtic's 'keeper had to be quick off his line to deny Akinola as he burst through from a ball in behind.
With 12 minutes to play, Akinola had a golden chance to put the Bees ahead but after beating his man he curled over the bar from inside the area. Moments later he had a half chance that was prodded towards goal but well saved by Wynne.
Currie's side continued to look the more likely as Mason-Clark saw an effort at goal blocked by one of a sea of white Farsley shirts. It was de ja vu moments later as Akinola's rasping effort was blocked again by the defenders, the hosts holding on as we entered the final five minutes.
We went within inches of the winner with four minutes to go as Mason-Clark skipped into the area but his effort went across the face of goal and didn't quite drop in.
Barnet: Loach, Alexander, Johnson, Reynolds, Dunne (C), Adams, Akinola, Fonguck (Vilhete 54'), Elito, Tutonda, Mason-Clark.
Unused Subs: Azaze, Sparkes, Edwards, Vasiliou, Box, Hernandez.
Charlee Adams, Medy Elito and Ephron Mason-Clark all came into Darren Currie's starting XI.
WHAT IT MEANS
The Bees will have to do it all again at The Hive London as we take on Farsley Celtic in a Second Round replay on Tuesday night.
It will be that replay with The Celtics on Tuesday night with kick-off 19:45 on Tuesday night. Ticket information for this fixture will follow in due course.