Lambert's side are sitting just above the drop zone after presiding over the club's worst start to a season in 43 years.
The 1-1 draw with Lambert's former club Norwich on Saturday left Villa with just one win from their opening nine games in the Premier League.
However, Lambert is not worried about the prospect of his side dropping out of the Premier League.
When asked about the prospect of Aston Villa being relegated, Lambert said: "They won't. There is a squad of players there I think can do it.
"We will stick together and keep driving it on. I trust the team, I trust the players to try and get results. It always hurts when you don't win. I just have this belief everything will be fine."
Lambert also insisted he has the backing of Villa owner Randy Lerner despite their struggles this season.
"I speak with the chairman all the time. We have a good relationship," added Lambert.
"He's very supportive. I don't have any problems there.
"He's behind the project we have here."