The Potters were officially relegated from the Premier League when they lost 2-1 against Crystal Palace last weekend.
Lambert, however, has issued a warning to those that could attempt to force a summer exit.
"Lads are under contract. It's not as if you can just walk out here and throw your toys out the pram and think 'I'm going to go.' You might not be going anywhere," Lambert told reporters.
"If the club keeps the core of the team and adds to it, adds guys that want to be here, the right type of player, the right type of mentality, the right character, then there's a great chance this club will bounce straight back up."
Stoke will look to move off the bottom of the Premier League table when they travel to Swansea City on Sunday afternoon.