The Spanish side look likely to face elimination from the Europa League at the group stage after a 3-2 defeat to the French side at San Mames.
The Los Leones head coach noted the whistles and boos that came from the crowd and fully accepted the fans' reaction, but he vowed to try and turn the club's form around.
"I consider it deserved and belated. We have been too patient and the patience had to do with the claims that the other defeats were unjustified," Bielsa told reporters this weekend.
"In the match against Lyon it was the time for this unworthy recognition. To build a new style is a laborious task that cannot be changed overnight.
"What was being castigated was not the style nor the current form, the public appreciates that they are progressing well, but what everyone feels right now is also appropriate.
"I believe that justice has been done. It has always been clear that we generated enthusiasm last season whereas what we have done this year is create disappointment."
Bielsa was speaking ahead of his team's game against Sevilla on Sunday and he remained a determined figure, despite Los Rojiblanco's underwhelming league form that has left them in 15th place after 10 games.
"This is a common scenario that I have faced countless times," the Argentine trainer added. "I do not want to brag about strength, but it is very difficult to stop fighting.
"It is much more likely that someone will decide on [whether to fire] me, rather than me choosing [to go]. When faced with adversity, I will always keep fighting."