Lambert is contracted to Villa until the summer of next year and Faulkner re-iterated that they are working together on a long-term plan for the club.
"We've got a really really good relationship, the three of us," Faulkner told the Birmingham Mail.
"Paul is a really good manager to work with. We have a view of where we want to try to develop and take the club forward and I think it's one that we all share.
"In any walk of life if you're in a working relationship like that it's a good place to be and you do feel like you can get stuff done.
"We know that football is a harsh, brutal business. Lots of criticism and stick will go flying all over. Everyone's got an opinion, everyone's an expert and they're entitled to that opinion and they're entitled to that.
"But being in the middle of it you've got to stay very strong and together and support each other. That's something that we are very good at doing.
"That makes you stronger and if you can keep doing it that allows you to actually grow and build."