But boss John Deacey knows his side should have returned from their trip to Wiltshire having secured all three points.
A late own goal by skipper Amjad Iqbal cancelled out Damien Reeves' effort that had put Celtic in front at the start of the second half.
"We deserved the three points, no doubt about it," said Deacey after his side had secured their second draw down south in five days.
Memory match slideshow - Farsley Celtic v North Ferriby 2006: Click here to enjoy picture slideshow."We created plenty of chances against a side that's done very well this year.
* Click here for Farsley Celtic match action picture slideshows."We came here looking for three points and we've done well but we've been undone at the end trying to play football in difficult areas of the park."
City custodian Ryan Clarke's man-of-the-match performance denied Celtic on a number of occasions.
After a scrappy first half at the rain-drenched Raymond McEnhill Stadium, Farsley took hold of the game almost immediately after the interval.
Stephen Downes burst down the right, causing City defender Matt Robinson all kinds of problems, before firing in a low cross which Reeves poked beyond Clarke at the near post.
Celtic pushed for a second goal but found the keeper in fine form.
Craig Bentham linked well with Reeves on 76 minutes, but the keeper was down quickly to save, while Rory Prendergast surged forward moments later but his fierce shot whistled just over the bar.
Salisbury made a double substitution in a bid to get back into the game and were certainly livelier with Luton Town loanee Rob Sinclair and leading marksman Matt Tubbs on the field.
Sinclair's 87th-minute cross for Darrell Clarke handed them a lifeline, the ball deflecting off Iqbal's head for the equaliser.
Now it was Farsley's turn to defend as the hosts forced three corners in a row after Wayne Turk's rasping shot was turned behind.
Still Farsley attacked and only another fine save by Clarke denied Prendergast.
But the home side finally showed why they had climbed to the play-off fringes in recent weeks and Curtis Aspden had to be alert to twice thwart Andy Sandell in stoppage- time as the hosts pressed for what would have been an undeserved winner.
City boss Nick Holmes admitted: "We were second-best for most of the afternoon.
"Farsley deserved to win and if they play like that for the rest of the season they'll be fine."
FARSLEY CELTIC: Aspden, S McNiven, Santos, Iqbal, Jackson, Prendergast, Krief, Bentham, Downes, Torpey, Reeves. Subs not used: Backhouse, Knowles, Stamer, Heath, D McNiven.
SALISBURY CITY: R Clarke, Bass (Sinclair 64), Cook, Asafu-Adjaye, Robinson, Bartlett, Turk, D Clarke, Sandell, Feeney, Barnes (Tubbs 64). Subs not used: Bittner, Bond, Brown.
REFEREE: Andrew Halliday (London).
ATTENDANCE: 1,081.
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