The Ukraine international made several outstanding saves as Real Madrid managed a narror 3-2 Copa del Rey win at Talavera.
Asked if he had just saved Xabi from the sack, Lunin replied: "I don't think that way. It's my job, what I've been doing since I was little. I have to help the team and always be ready.
"I don't know who could doubt Xabi; we don't doubt our coach. We're a team, and we're all in the same boat. I don't know who's questioning him, whether it's the fans or the press, but in the end, it doesn't matter to us because we're focused on our job."
Regarding what has changed at Real Madrid since Xabi replaced Carlo Ancelotti, he added: " You have to understand that every coach is different. Ancelotti was older, more experienced, and had won everything in his career.
"Xabi is young, everyone respects him, there are new developments, and it's a normal process of adaptation and change."