Abel Resino's side have had a poor start to the season and struggled to create openings in the first half, while Constantinos Charalambides squandered two glorious chances for the visitors.
Sergio Asenjo produced a superb save to deny the APOEL striker in the eighth minute and the same player sidefooted wide when he had the goal at his mercy just before halftime.
The Atletico faithful vented their frustration at the break and although the home side came out with more purpose for the second period and several times came close to scoring they could not find a winner.
Diego Forlan struck one long-range shot against the post and, when the Uruguayan was denied near the end by an acrobatic save from Dionisios Chiotis, Simao Sabrosa should have put the rebound in but skewed the ball wide.
Earlier, Sergio Aguero just failed to get on the end of a cross from substitute Maxi Rodriguez and Jurado also forced a good save from Chiotis as APOEL held on to the delight of several hundred orange-clad fans at the Calderon.
EXTRAORDINARY SAVES
Resino said his players had found it hard to get into the match and refused to criticise them.
"We played very well in the second half but their goalkeeper was very good and we were short on luck," he told a news conference.
"This result was not part of our plans so we have to go to Porto now and get three points," he added.
APOEL coach Ivan Jovanovic bemoaned his players' wayward finishing but praised Chiotis.
"He made some extraordinary saves from Forlan, one of the best forwards in Europe, and that means his effort is all the more valuable."
Chelsea beat Porto 1-0 in the other game in the group.
