Needing a win to keep their hopes of a Europa League place alive, the Bhoys got off to the perfect start with Giorgos Giakoumakis's goal, but a brilliant equaliser from Mykhaylo Mudryk rescued a point for the visitors.
Ange Postecoglu's side could afford to play without fear in front of their own fans and pressed high right from the first whistle, albeit without the desired ruthlessness in front of goal.
Shakhtar began to get a foothold into the game and always sought to get the dangerous Mudryk on the ball, but Celtic would end up drawing first blood in the 34th minute.
Liel Abada picked up the ball in the box from Sead Haksabanovic's pinpoint low cross from the left - his shot was blocked, but the ball fell kindly for Giakoumakis in acres of space to lash home the rebound into the bottom corner.
Celtic had their tails up after Giakoumakis's goal, and the Greek was afforded all the time and space to let fly from distance in the 39th minute, and it took a good save from Anatolii Trubin to prevent his strike from nestling into the bottom corner.
Joe Hart was forced to prevent Mudryk from levelling for Shakhtar in the dying embers of the first half after the highly-rated attacker broke through, but Celtic got to half time with their one-goal lead intact.
Postecoglu's side received a huge let-off just after half time, though, as a quick Shakhtar break ended with Lassina Traore playing the ball across to Oleksandr Zubkov, who could only hit the side netting while on the stretch.
Shakhtar would eventually get their reward through their attacking sensation Mudryk, who had worryingly gone down injured a few moments beforehand, but he dusted himself down before surging forward and firing home a bullet of a strike into the roof of the net from outside the area.
Mudryk was here, there and everywhere from Shakhtar and deserved an assist when he led a rapid counter-attack from the visitors in the 72nd minute, but after seemingly laying the ball on a plate for Danylo Sikan to tap into an empty net, the substitute inexplicably took a heavy touch and watched the ball trickled harmlessly wide of the post.
Sikan's blunder would arguably go down as one of the worst Champions League misses of all time, and the game had a very open feel to it in the dying embers as Celtic pressed for a winner.
Hoops heads were in hand when Matt O'Riley side-footed a half-volley just wide of the post on the 88-minute mark, and Celtic's winless run in the Champions League went on as they were condemned to a fourth-placed finish.
Postecoglu's side now travel to face Real Madrid with nothing on the line next week, and their Ukrainian counterparts face a winner-takes-all clash with RB Leipzig after the German giants stunned Los Blancos to remain one point above Shakhtar in second place.