Failure to win at Reading on Saturday would make relegation all but inevitable and Hodgson knows his impressive CV, which has seen him in charge of the Swiss and Finnish national teams, will be blotted as a result.
He said: "Any manager whose team gets relegated, irrespective of whether he has come during the season, will have to say he has failed.
"I signed a contract and am not the kind of guy who walks out on things so, as far as I am concerned, if they want me to stay then I will be fulfilling my contract.
"When I signed I was fully aware I was taking on a job where this could happen.
"It wasn't looking great but if I had only been interested in giving it a shot at keeping them up then I wouldn't have signed to the end of next season."
He said: "Apart from Bristol City, where we were forcibly relegated by the situation, and Blackburn, who were in the bottom three when I left but I wasn't the person who took them down, I haven't had a relegation.
"I have had a lot of promotions and UEFA qualifications but not relegation.
"But we are where we are because we haven't scored enough goals, we have let too many goals in and we haven't got enough points. The league table does not lie."
He said: "I signed a contract to be here next season but it is not up to me. If the club decides they want to get rid of me then they will do so.
"They have got rid of other managers in the past and I am not saying I have a God-given right to be here.
"What I am saying is that I don't turn my back on things. I didn't sign the contract I signed when I first came to Fulham to walk out if I didn't get all the sweets I wanted in my first few months here.
"I came here to be manager of Fulham Football Club and that is what I am still doing to the best of my ability."