England survived a first-half mauling by Brazil, who had 30 shots - 20 at goal - while the visiting side managed eight in response, seven of which were on target. Brazil had taken the lead through Fred, before England stunned the Maracana crowd to go 2-1 in front, before Paulinho's outstanding volley levelled the scores.
"The simple answer is that I do think we were well worthy of the draw," Hodgson said.
"I was delighted with how we kept ourselves in the game and didn't capitulate despite them being clearly better than us in the first half. In the second half we were every bit as good and we should take lot of credit for that. The shot statistics weren't raved about in the Ireland game - the complaint was that we didn't win.
"Most teams, managers and coaches know that when you come to Brazil and play them they will have more of ball and create more chances. The question is if you can deal with it and come away with a result and that's what we did."
Keeper Joe Hart was England's outstanding player but the goals were both worthy strikes to light up the Maracana.
Hodgson added: "Joe was busier than normally is. In the first half he made some good saves and was very good at supporting the defence. The pitch was not very fast and meant ball held up. Our first goal was one that pleased us because of build-up by Wayne and then the strike. Then for the second Wayne is always dangerous cutting in. Maybe there was a little deflection but even without that it still would have had Julio Cesar at full-stretch."
Brazil coach Luiz Felipe Scolari said he had shaken Hodgson's hand and wished him good luck to return for the World Cup next year - but he also bemoaned his side's profligacy in front of goal.
Scolari said: "I hope England come to the World Cup. When I spoke to Roy just now I said I hope to see you at the World Cup and that we will meet again. But we know in Europe that is difficult, much more difficult than qualifying in South America where we have four or five from 10 teams."
Scolari said Brazil paid the price for not taking their chances in the first half, adding: "In this match England had only seven shots and scored twice while we had 30 shots altogether and only scored two goals. So something wasn't working in our attempts on goal. We have to take advantage of the opportunities when they arise."