Villa fans called for Lambert to be sacked during a 1-0 Premier League defeat at struggling Leicester City on Saturday.
A run of six league games without a win - and four without scoring - has left Villa just three points above the relegation zone in 13th place.
Guzan is well aware of discontent among supporters and believes the players must take responsibility for their disappointing form.
He said: "When you go through difficult times everyone has got to take their criticism. The manager has been brilliant in defending us but we are the ones who have to score goals.
"He can't go and score for us, the assistant manager can't score for us, the goalkeeping coach can't score for us.
"Us as players have to take responsibility and I know the fans are unhappy, we hear them during the game, but they need to realise it's a difficult moment and we need to stick together.
"Regardless if they are unhappy with the manager or situation, we need to stick together because it's about the club.
"It's our job to defend, save shots, score, tackle, head pass - it's our job."
Villa host Liverpool on Saturday.
