Fans voiced their disapproval with choruses of boos at the end of a calendar year which has seen Villa win only three home league matches.
Lambert, who took over in the summer, said: "The fans since I have been at this club have been brilliant, totally fantastic with myself and the team.
"I can understand them (booing). I would never criticise the crowd here that's for sure, they have been fantastic.
"All we can do is do our very best for this football club. The fans will go away hurt like everybody else, so will we.
"I know that for a fact. But we have to stick together. That's important."