Tigana quits as Bordeaux coach
The former Fulham boss, who also offered his resignation in February but it was refused, presided over a disappointing season at the 2009 champions who are ninth in Ligue 1.
"It's a disastrous evening for the club and for me," Tigana told a news conference.
"My daughter was verbally abused in the stands. She has already had problems at school. I have therefore taken my decision. I quit my role at Bordeaux."
The 4-0 humiliation has left Bordeaux four points adrift of a possible Europa League berth with four games to go.
Tigana, who took over at the start of the season when Laurent Blanc left to manage France, were not helped when Bordeaux sold top playmaker Yoann Gourcuff to Olympique Lyon in August.