Grenier had been given the chance to open the scoring from the spot earlier in the half, and he feels that his error cost Lyon a point.
"My penalty miss was the turning point of the match," Grenier told reporters.
"Despite losing at home, it is only at the beginning season and we have a return match Wednesday in the Champions League [against Real Sociedad].
"We cannot talk about a nightmare start to the season right now and we will recover."
Lyon will be looking to overturn a two-goal deficit when they face Sociedad in the return leg of their Champions League qualifier.