Wayne Rooney's second-half penalty saw the Three Lions bounce back from a horrid World Cup campaign in Brazil, which saw Hodgson's men depart the tournament winless after three group matches.
But the 67-year-old was frustrated by criticism of their first friendly since that debacle, taking umbrage to journalists citing the statistic.
"Listen, I am entitled to [praise the performance], 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 says that 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?" he continued. "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 that he cannot change the effect that the World Cup performance has had on his side's image but 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," the former Liverpool boss remarked. "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."