But the "devastated" coach conceded his employers the Football Association could rethink his position following his team's devastating 2-1 loss to Uruguay in Sao Paulo yesterday.
"I'm bitterly disappointed, of course, but I don't feel I need to resign, no," 66-year-old Hodgson told British broadcaster ITV. "On the other hand, if the FA think I'm not the right man to do the job..."
Hodgson said Luis Suarez's late winner, his second goal of the night, was an "unbelievable blow" after England worked their back into the game with a Wayne Rooney equaliser.
"We are more than disappointed, we're devastated."
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Hodgson said he was also taken aback by the manner of Uruguay's winner, which came when a speculative ball from goalkeeper Fernando Muslera skidded off Steven Gerrard's head and into the path of Suarez.
"It was a goal we don't expect to concede. Long goal kicks with the type of players we have in the team, we deal with them," Hodgson said.
- 'Unbelievably slim' -
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A stony-faced Hodgson admitted England's chances of staying in the World Cup were "unbelievably slim" as they face their first exit at the group stage in a World Cup since 1958.