After claiming three victories in their opening four matches of the campaign, Villa have managed just two wins since and find themselves three points above the relegation zone.
Saturday's 1-0 defeat at Leicester - Villa's sixth successive match without a win - saw Lambert's men fail to find the back of the net for the 12th time in 21 games.
Supporters turned on Lambert at the Walkers Stadium, but Guzan insists the players are the ones at fault.
"When you go through difficult times everyone has got to take their criticism," he told the Birmingham Mail.
"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 and the coaching staff can't score for us.
"Us 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 for the players and fans but we need to stick together.
"Regardless if they are unhappy with the manager or situation, we need to stick together and work hard in training because it's about the club.
"We are trying to score goals. We're not purposefully going out there saying: 'Let's just keep the ball and forget about trying to go forward'."
A daunting run of fixtures awaits Villa, with Liverpool, Arsenal and Chelsea representing their next three Premier League opponents.
