The Aussie international returned to Elland Road this week after visiting his father and is ready for the battles to come.
He told the club's official website: "Things are difficult now but we're going to give it our best shot. There's nothing else we can do.
"Either we feel sorry for ourselves and start to drop or we can keep believing. Basically there is nothing to lose, we just have to fight for every game.
"I hope that is the spirit among the other players. I've only been back a few days, but I hope it is.
"I hope we can all realise that it is up to us to fight our way out of this trouble."
Viduka also revealed he had a mutual agreement with The Whites not to leave the club during the Premier League's January transfer window.
Despite speculation over a move to Middlesbrough, Viduka pledged to return the loyalty Leeds showed to him during his three-week absence to be with his sick father in Melbourne.
He denied reports he had been seeking a move during last month's transfer window.
"I would like to thank Eddie Gray, Trevor Birch and the staff and fans of Leeds United for the understanding and compassion shown to my family and me during these difficult last few weeks," Viduka said.
"Contrary to media speculation, it was mutually agreed that I would not leave the club in this transfer window and I am happy that I have the opportunity to repay the club on the pitch as we battle against relegation."