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. (Agencies)
"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," he said.
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 believed we could do enough to get a result in this game. Having worked so hard to get back to 1-1 I believed we would go on to win the game or at least draw, so to concede the second goal is an unbelievable blow. I don't really know what to say at this time. We are more than disappointed, we're devastated," the coach said.
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.
England also lost their Group D opener 2-1 to Italy, leaving them relying on the Azzurri beating Costa Rica on Friday to keep their hopes alive in the competition.
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.
The downbeat England boss said his team managed to keep Suarez, who was returning from knee surgery, quiet for long periods but Gerrard's late error let him in for the winner.
"We're normally used to seeing him a lot more active around the penalty area than we saw today,” he said.
"The second goal as you probably saw was an unfortunate flick off Steven Gerrard's head which put him free with the goalkeeper. And when he comes free with the goalkeeper he doesn't miss from that area,” the coach said.
"Ideally your only plan to deal with that would be to make certain that you don't allow the flick to put him through and free with the goalkeeper," he added.
Hodgson added: "Two chances came his way and as the top player he is, he took both chances -- and probably ended our chances of staying in the competition."
But the manager was upbeat about England's future, pointing to his crop of young players.
"I believe the team going forward will be a very good team," he said.
"Results colour everything. We played against a very tough tackling, strong defensive Uruguayan team but I don't think we need to have any doubts that this England team, this group of players will do some good things in time," the manager said.
Goalkeeper Joe Hart spoke of his respect of Hodgson, despite the disappointing results in Brazil.
"I'm proud to play for Roy Hodgson. He's a great manager. He's a very passionate man," he said.
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.