Dyche was one of the favourites with bookmakers to become the Dutchman's successor, a job Sam Allardyce subsequently landed.
When asked if he felt he may have dodged a bullet by not landing the Everton job, Dyche said: "There was no bullet to dodge.
"I was here, I said I was going to be here, and I'm still here. It was an outside story. I've had a few of them, in the right way actually, since I've been here.
"This is my 250th game. I'm still here, I'm still working hard, and I still have the fire in my stomach to be successful here and to continue to create an atmosphere and a culture and environment that can be successful. That is my focus."