Having fallen behind, goals either side of half time from Jonathan Drake and Blessing Adaleye had put the Wrens in the driving seat, before a late penalty gave the Tevie Boys a share of the spoils.
Speaking after the match, Saxby admitted: "As far as we are concerned it was a massive throwaway. Anyone walking into our dressing room after the match would have thought we had lost and given away three points, so all the lads were disappointed."
An injury to debutant captain and man of the match Aidy Harris may have been the turning point to some extent, but Saxby was frustrated by the manner in which both goals were conceded.
He continued: "The first goal was clearly offside, and the linesman raised his flag and then dropped it, while the second, a penalty, was the result of a needlessly rash challenge.
"Aidy's injury was a recurrence of one he has been carrying, and we hope it's not too bad. We will have a look during the week whether he is ok for next Saturday against Clifton and go from there.
"The positive thing for us is that we have taken four points from our first two games in charge, doubling our tally for the season, and if someone had offered us that when we started we would have snatched their hand off. And it's also a positive in that our frame of mind is such that we are disappointed to draw, and see it as points lost rather than one gained."
Looking forward to Saturday's home fixture with Clifton, kit remains to be seen whether Harris will be fit, but forward Sam Asuman should be available after missing the Teversal game, and Saxby is hopeful of having a new centre half in place who has experience at a higher level.
Clifton have won five of their last six, two of them by double figure scorelines, so it will be a searching examination of Saxby's new look squad.
Updated 09:40 - 30 Aug 2019 by Gordon Foster