Scotland midfielder Kris Commons scored a brilliant looping volley from Charlie Mulgrew's free-kick to give the Scottish champions a deserved lead on 40 minutes before limping off injured with 15 minutes remaining after Inter's Samir Handanovic had swatted his shot over the bar.
With Celtic down to 10 men having used all their substitutes, Inter equalised with one minute left when substitute Rodrigo Palacio forced the ball home from Marko Livaja's cutback after home goalkeeper Fraser Forster had made a brilliant stop to deny Diego Milito.
Celtic manager Neil Lennon will hope Commons can return to face Helsinki in the first leg in Glasgow while there is also a concern over Republic of Ireland forward Anthony Stokes after he was carried off in the first period attempting to block an Esteban Cambiasso pass.
"The next 24 hours will be important, to see how they react. I think Kris would be a bigger doubt that Anthony at the minute," said Lennon.
"We will give them as long as possible to see if they can recover in time for Wednesday."
Celtic need to negotiate two qualifying rounds to return to the Champions League group stages for the first time since 2008.
Celtic: Forster; Matthews, Lustig (Irvine 66) Mulgrew, Izaguirre; Commons, Wanyama, Ledley (McCourt 66) Samaras (McGeouch 73) Hooper (F. Twardzik 66) Stokes (Bangura 36)
Not Used: Zaluska