Villa missed out on a Wembley appearance after their Capital One Cup failure against Bradford City.
Lambert is adamant he remains the right man for the job of rebuilding Villa.
He said: "Am I still the man for Villa? Yes, absolutely. When you ask managers that, they will tell you they just get on with it. Until you hear anything different you have to run with it.
"There are two ways - you either lie down and take it or you come out fighting. I am certainly not going to lie down."