The under-fire Kop boss, who signed a megabucks five-year deal last March, said: "Leaving has never gone through my head - clearly I want to fight.
"I signed a long-term contract and have belief in this club. Inside, I am as strong as ever."
The FA Cup exit to Reading sparked a flurry of calls for Benitez to be axed, with even Reds legend Ronnie Whelan calling for his head.
Yet Kop powerbrokers were quick to insist his job is safe, backing the Spaniard after the third-round debacle, despite their Champions League KO and slide out of the title race.