Lambert expressed his disappointment at conceding so late on, but believes that his side will avoid relegation if they continue to perform like they did this afternoon.
"I thought we deserved to win the game. You are never going to get an easy game here but it is disappointing to only get a point," said Lambert.
"It is a really tough place to come and three points would have been great but I thought we played ever so well. I can't fault the way the lads played and there are not many teams that come up here and beat them.
"David [Moyes] has a really good side but if we continue to play like that hopefully we will start to get results."
The result leaves Villa languishing down in 19th place in the Premier League table, two points adrift of safety.