In a game with few chances, the Israelis looked as good as their illustrious Spanish opponents and showed great discipline in defence.
Maccabi were also unlucky not to be awarded a penalty in the 15th minute when former Derby striker Nick Blackman was booked for a dive but replays show he was actually fouled.
Maccabi manager Jordi Cruyff said: "We were organised in defence but didn't make enough effort to score.
"If we would have been sharper going forward we would have scored but I can live with this result."
Having lost 0-1 to Slavia Prague on Matchday One, the results leaves Maccabi three points adrift of Villareal and Slavia and tied with Kazakhstan's Astana.
Maccabi now faces a crucial double-header with Astana.
Hapoel Beer Sheva lost 3-1 to Plzen in the Czech Republic . Plzen took the lead in the 29th minute through Milan Petrzela but Maccabi equalised in the second half with an excellent Tony Nawkaeme strike before two late goals won it for Plzen.
"We conceded easy goals when we had to momentum in the second half," said Hapoel manager Barak Bakhar.
Having beaten Lugano on match-day one, Hapoel are tied second in Group G with Plzen on three points and now face a doubleheader against group leaders Steaua Bucharest.
Hapoel Beer Sheva defender Shay Tzedek failed a Uefa drug test after the Lugano match and could face a lengthy suspension.
