Chants of 'We want Lambert out', 'You don't know what you're doing' and 'We want our Villa back' emerged during defeat to Leicester City.
"When you go through difficult times everyone has got to take their criticism," he 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 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'."