Mason Mount's double gave the visitors a win that heaped more pressure on Gerrard, whose side are 16th in the Premier League and one point above the relegation zone.
"I think I'd be stupid not to concern myself or be aware of where we are and I accept that," said Gerrard.
"Every time I've spoken to the media, I've fronted up and I won't hide from the responsibility, the criticism or the noises that are coming from the stands today.
"But what I will say is, if these players can replicate that first hour moving forward, I don't think this team will have an issue and they certainly won't be in the area they are now in the league."
Former Liverpool skipper Gerrard was also booed off the pitch by Villa supporters following a 1-1 draw at bottom side Nottingham Forest earlier this month.
Gerrard said he understood the frustration of the fans after Villa created several good chances against Chelsea before the break only to be frustrated by goalkeeper Kepa Arrizabalaga.
"I'm aware of it all, but it is what it is," Gerrard said.
"I have to accept it and try and do everything I can to change the way they're feeling at the moment."
