The Three Lions suffered a blip in their efforts to reach Brazil on Wednesday evening when they were held to a 1-1 draw against Poland in Warsaw.
Despite the draw, they are still top of Group H after four matches.
"If it's a dogfight, it's a dogfight. There's nothing wrong with that," said Hodgson. "The good thing is we know we can stay and take part in a dogfight.
"We took part in a few dogfights during the Euros and we certainly dug in against Poland and showed the right sort of character and determination."
Hodgson's side have friendlies against Sweden and Brazil before they resume their qualifying campaign in March 2013.