Natalia Arroyo said the result was a "cruel" welcome to the league, while Chelsea boss Sonia Bompastor admitted her side benefitted from "a lucky win".
For 82 minutes Aston Villa went toe-to-toe with the champions at Villa Park with Sarah Mayling's unfortunate own goal the difference between the two sides.
Arroyo's Villa team looked unrecognisable from the side that started the WSL season with just two points from their opening six games.
Interim boss Shaun Goater has steadied things in recent weeks, leading them to two wins from his five matches in charge.
And against the reigning WSL champions in Arroyo's first match in charge Villa produced their best performance of the season and almost took the lead in the second half when Kirsty Hanson struck the underside of the crossbar.