Brendan Rodgers will be disappointed his side were unable to take a lead into Tuesday's second leg after the Greek side had midfielder Kostas Galanopoulos sent off in the 57th minute for a second yellow.
Callum McGregor had fired Celtic in front in the 17th minute with a well-struck effort on the turn from a tight angle but AEK drew level a minute before the break through Viktor Klonaridis.
After losing Galanopoulos, who seven minutes after being booked picked up a second yellow, AEK sat deep and defended and were able to frustrate Celtic.
The winners of the tie will face either Sweden's Malmo or Hungarian team Vidi in the playoff round with a place in the group stage up for grabs.
Greece's other Champions League hopefuls, PAOK Salonika, came back from two goals down to beat Spartak Moscow 3-2 in a thrilling game.
Goals from Ivelin Popov and Dutch winger Quincy Promes put visitors Spartak 2-0 up inside 17 minutes but the Greek side responded quickly.
A penalty converted by Aleksander Prijovic got PAOK back in the game in the 29th minute and goals for Dimitris Limnios and Dimitris Pelkas put the home side 3-2 up by the break.
Spartak had a great chance to level after the break but Promes's 71st-minute penalty was saved by PAOK keeper Alexandros Paschalakis.
The winners will play Portugal's Benfica or Turkey's Fenerbahce in the playoff round for a place in the group stage.
Austria's Salzburg enjoyed a comfortable 3-0 win over Macedonian side Shkendija with two gals from Israeli forward Moanes Dabour.
Should they complete the job in the second leg, Salzburg will face Red Star Belgrade or Spartak Trnava in the playoff round.
(Reporting by Simon Evans, editing by Pritha Sarkar and Ed Osmond)
Share
