A 2-1 defeat to Luis Suarez-inspired Uruguay on Thursday leaves England with no points from their opening two Group D fixtures.
They must now rely on results elsewhere to reach the last 16, but Hodgson is determined to lead the team into qualification for UEFA Euro 2016.
Several youngsters have made the trip to the Brazil showpiece, including Ross Barkley, Luke Shaw and Raheem Sterling.
And Hodgson, while conceding England's hopes of escaping the group are fading fast, believes the strides made by the players in recent weeks is enough to convince him he remains the man for the job.
He said: "I don't have any intention to resign.
"I've been really happy with the way the players have responded to the work we've tried to do.
"I'm bitterly disappointed, of course, but I don't feel I need to resign, no.
"On the other hand, and if the Football Association think I'm not the right man to do the job, that will be their decision and not mine.
"Our chances are unbelievably slim now.
"I think in both the games we've shown some elements of playing good football, and shown we are a team that's making progress. But results decide everything and both results have been negative."
