Speaking in the wake of his side's 1-1 draw at West Ham United, the Potters boss said that his team need to take maximum points off the Clarets this Sunday to boost their chances of avoiding relegation.
"Beating Burnley is a must-win, they're a good side, but I'm really proud of the team, and if we keep doing what we're doing then we'll put ourselves in the mix," Lambert told Sky Sports News.
"I believe we can do it, I honestly do. I can't fault the effort or commitment, and we'll see what happens."
Stoke are second from bottom of the Premier League, five points from a position of safety following their draw against West Ham.