Michael Ciani's first-half header earned Laurent Blanc's side a vital victory on Tuesday that makes the French clear favourites to reach the quarter-finals ahead of the return leg at the Stade Chaban-Delmas on March 17.
However, the Greek title-holders, who produced one of their better European displays, were left cursing their luck after missing a flurry of second half chances before Webb disallowed Maresca's header in the closing seconds.
English striker Matt Derbyshire was adjudged to have fouled Bordeaux goalkeeper Cedric Carrasso in the build-up but television replays suggested little evidence of a foul.
Derbyshire also looked as if he was being held by Ciani as he attempted to challenge for the ball when Carrasso rushed out to gather it, tumbling over both players.
"From the pitch it's difficult to be sure but I consider that the referee made a mistake in disallowing the goal," Maresca told reporters.
"We limited their play and created at least four classic opportunities to score but that's the way it goes sometimes in football."
"The goal should have counted, there was no foul," added former Portsmouth striker Lomana Lua Lua, who was guilty of missing two great chances to level the score in the last 10 minutes.
"The result is unfair on us. We limited Bordeaux to only a few chances while we created many more and I believe we can achieve something good in the second leg."
Vasillis Torosidis was more damning in his assessment of Webb's display.
"I think the referee was confused, he thought we were playing against an English team, but Bordeaux is French," said the defender.
"Perhaps he was a Bordeaux fan as a child. That's football though and this time we were the team who suffered an injustice."
