The Scottish champions got off to a fine start against Shakhtar Donetsk as Reo Hatate's shot found its way into the net, via Shakhtar's Artem Bondarenko.
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However, Mykhaylo Mudryk's 29th-minute equaliser saw both sides share the spoils in Poland.
Mudryk begun his professional career with Shakhtar and the 21-year-old winger admitted that it would be hard to turn down an offer from a Premier League club, namely Arsenal.
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Speaking to CBS Sports in August, the Ukrainian said: "I think every guy dreams about the Premier League. It's hard to say [who his preferred move is] but Arsenal is a very good team, very good coach, I like the way they play."
When asked if he would make a move to the Emirates Stadium he said: "From my side, I can't say no [to Arsenal]. But the transfer is not only my decision."
Ange Postecoglou's men survived some more pressure before reasserting their superiority after the break.
However, substitute Giorgos Giakoumakis missed the best in a series of opportunities for Celtic to claim their first European win of the campaign.
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Having also squandered chances during their opening defeat by Real Madrid, Celtic now face another trip to RB Leipzig on October 5.