The Israeli league leaders lost 1-0 to Girondins Bordeaux, who recorded a fifth successive Champions League victory despite fielding a second-string side.
Brazilian Jussie scored the only goal of the match from the edge of the area in the 13th minute.
Try as they might to score the solitary goal that might have earned them a draw, the Haifa side lacked clear direction in attack and failed to mount a single credible assault on the Bordeaux goal.
Haifa were making their second appearance in the group stages after making their debut in 2002 when they defeated Manchester United and Olympiakos.
Jussie could have added a second goal two minutes after scoring his first with Haifa goalkeeper Nir Davidovich off his line and the goal at his mercy but his soft shot was scrambled off the line by defender Dekel Keinan who dived desperately.
The match also marked a farewell for veteran Haifa defender Alon Harazi, 38, who retired in his 720th appearance for the Israeli club. He will begin an administrative role for Haifa.
The former international who came on in the 71st minute played 89 times for Israel, second only to Arik Benado of Beitar Jerusalem who made 94 appearances.
Bordeaux coach Laurent Blanc said he was pleased with his players' performance and thought they deserved to win but added that Haifa were not as weak as their record showed.
TOUGH OPPOSITION
"My team dominated this evening against Haifa but when you look at their matches against Juventus and Bayern Munich they posed them problems and they posed problems for us in Bordeaux," he told reporters.
Blanc said after Bordeaux had been drawn in the same group as Juventus and Bayern they were the outsiders but their performances showed that they had deserved to win the group.
Haifa coach Elisha Levy said his team had had performed well but had had to face very tough opposition.
"I think the team has had a good campaign although we once again found ourselves in a very tough group, we play in a very small league," he said.
He added that he had kept faith with the young side who had won the league title and that buying more players would not have changed the overall result.
"Perhaps an additional reinforcement could have scored a goal but it would not have changed the outcome of our campaign," he said.
