The travelling supporters called for Lambert’s head for the second straight game as they lost 1-0 at Leicester on Saturday.
Villa have won just twice in 17 Premier League games and sit three points above the drop zone following Paul Konchesky’s winner.
They are the lowest scorers in the top four divisions with just 11 goals in 21 games.
Lambert is under increasing pressure, but Guzan insists it is not all his fault.
“When you go through difficult times everyone has got to take their criticism,” the keeper said.
“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.
“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.”
Ciaran Clark was sent off — Villa’s fourth red card in six league games — after clashing with Matty James, who was also dismissed, in injury time.
Konchesky’s strike could not lift the Foxes off the bottom of the Premier League but they are now just three points from safety. They are unbeaten in four games in all competitions and were watched by striker Andrej Kramaric as he waits to complete a club record move from Croatian club Rijeka.
He will have a work permit hearing this week and boss Nigel Pearson is anxious to seal the deal.
“We’ve not heard any more from where we were. It’s wait and see this week. The hearing’s this week,” he said.
LEICESTER: Hamer, Simpson, Wasilewski, Morgan, Konchesky, Albrighton (Lawrence 72), Hammond (King 75), James, Knockaert, Nugent, Ulloa (Vardy 72).
ASTON VILLA: Guzan, Hutton, Okore, Clark, Cissokho (N’Zogbia 89), Cleverley, Westwood, Sanchez (Richardson 76), Agbonlahor, Benteke, Cole (Weimann 72).
Referee: Michael Oliver.