The pressure has increased on the Scot following Villa's loss at the New Den, coupled with the humiliating exit in the semi-final of the Capital One Cup at the hands of League Two outfit Bradford City.
The Midlands club are also performing poorly in the Premier League, as they sit just one place above the relegation zone.
However, Lambert, who took the job in the summer, said that he will not walk away.
"I will keep on fighting," said Lambert. "The blows keep on coming but there are two ways you can deal with it.
"You can accept it, or you can come out fighting."
Villa entertain Newcastle United at Villa Park on Tuesday.