Wayne Rooney's second-half penalty saw England bounce back from a horrid World Cup campaign in Brazil, which saw Hodgson's men depart the tournament winless after three group matches.
However, the strain seemed to be getting to the 67-year-old when asked if he was put off by the question inquiring about his thoughts on the stat showing England's lack of aggression.
"Listen, I am entitled to, aren't I?" he said.
"When you have questions like, 'You only had two shots on target...'
"I can't put the World Cup right, because I can't turn the clock back. What I can do is analyse what I have seen and judge that through my eyes and not judge it because someone is going to tell me, 'Well, you only had two shots at goal'.
"Because for me, that is absolute f***ing b*****ks, I'm sorry."
Hodgson said the stat was biased by the fact the Norwegian defence blocked a lot of their chances.
"Don't give me that one, I mean, two shots on target?" said Hodgson.
"What about all the shots that they threw themselves in the way of in the first half? Don't hit me with statistics - you use them if you like.
"You have just seen an England team dominate for 45 minutes against a good opponent, an opponent that's hard to beat, and you have seen them work very hard to create chances.
"I would have liked to have seen Daniel Sturridge's magnificent effort from that wonderful pass that played him in from Raheem Sterling not land on the roof of the net, but the fact is that is what you have to accept as a football manager."
Hodgson acknowledged he cannot change the effect the World Cup performance has had on his side's image, but he wants to work on improving it as they embark on a Euro 2016 qualifying campaign.
"All I am saying is I want to judge every game as it is," he said.
"We can't get rid of the baggage. We can't change the fact that we had a bad World Cup. We can't play those games against Italy and Uruguay again.
"But I think you will have to give me the entitlement at least."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.