Paulo Sousa's side remain second in Group F with eight points following the stalemate - the same result played out between the two sides in the reverse fixture at Bloomfield Stadium on September 19 - ahead of their final group clash against Bordeaux next month.
Third-placed Apoel, meanwhile, remain three points further back and with a worse goal difference to Maccabi with a match to come against Group F winners Eintracht Frankfurt.
The away side started well and Maharan Radi's cross was cleared by Nuno Morais before it could amount to anything.
Apoel could have taken the lead minutes later as they were awarded a free-kick after Carlos Garcia was penalised for a foul on Athos Solomou. Konstantinos Charalambidis took the set-piece but Marcelo Oliveira's header sailed over the crossbar.
Midway through the first half Efstathios Aloneftis had his cross-shot tipped over the bar by Juan Pablo as the home side pushed for the opener.
Maccabi striker Barach Yitzhaki came close 10 minutes before the break but his shot from the centre of the Apoel area failed to hit the target.
The home side continued to search for an opener after the break and Nektarios Alexandrou was unfortunate just before the hour when his close-range shot just missed the right-hand post.
Juan Pablo was again called into action as Esmael Goncalves' 25-yard effort came close to breaking the deadlock moments before Alexandrou had a chance with a close-range shot which he fired over the bar.
Maccabi had not given up yet and Tal Ben Haim had the final chance of the contest with a beautiful shot from the left of the 18-yard box that forced Rafael Urko to tip around the post.