Valverde was speaking ahead of tonight's Copa del Rey quarterfinal against Valencia - a tie Athletic are expected to win.
He said, "Since I've been here, I've always felt the confidence of the previous presidents and the people at Lezama, which is guaranteed at Athletic.
"It's always like that, whether I'm the coach or someone else is . But I'm well aware that in football you have to win, and results are what matter.
"I don't pay attention to what's going on around the club: I know that if you win, everything is sorted out, and if you lose, the coach gets blamed, but it's something I accept."
Athletic sit 11th on the LaLiga table and Valverde added: "The transition has been done at full speed. You can't forget what you have to do.
"The League is long and it's true that sometimes we can't explain why we let games slip away, but if it happens repeatedly, it means we have to look at it because something is wrong and there's a deficit that a team like ours can't afford to have.
"I feel responsible because I'm the coach."