A late own goal from Villa’s Sarah Mayling helped the Blues continue their unbeaten run in the Women’s Super League this season.
The five-time defending champions hold a seven-point lead at the top of the WSL and have conceded just six goals in 13 matches – all of which Bright has played in.
The 31-year-old asked for fans to be “more mindful of your comments”.
“After every game we as players make a choice to give you our time, support and generosity to do photos, signatures, have conversation, because we care and respect you travelling to support us,” she added.
“Every game we give our absolute all and it won’t always be pretty or perfect, but just remember we give everything to be the best for you. So this experience was hugely disappointing, especially from a fan sat in the Chelsea section.”