Lambert's assistant boss Roy Keane described the Portuguese coach as "disgraceful" for offering his hand with around three minutes left of Villa's 3-0 defeat to play at Stamford Bridge.
When asked by reporters if he thought Mourinho was being disrespectful, Lambert said: "Yeah I do, yeah. My thoughts are exactly the same as Roy's on them. The game has not even finished. I just thought it was wrong. It's not the way I was brought up."
Both Lambert and Keane, who said that Mourinho would have got "knocked out" for that kind of behaviour in Sunday league football, refused to shake his hand.