The All Blacks posted their 13th victory of an unbeaten year with a 30-22 win at Twickenham, but they were forced to dig deep in a compelling Test.
"I was annoyed with everyone saying we were underdogs - 'All Blacks this, All Blacks that, maybe England aren't good enough yet'," Vunipola said.
"But we showed against them that we are good enough by pushing them as far as we did.
"I was pretty happy that they kicked the ball to me straight away.
"After watching the Haka and seeing them, I just wanted to get the ball and go at them.
"They kept kicking the ball to me and I was more than happy to take it!"
England's performance suggests they can be genuine contenders at the 2015 World Cup and they have another four meetings with the All Blacks over the next 12 months in which to gauge their progress.
"We can be a massive force in two years' time. We've got a good team and coming to Twickenham is a pretty daunting task," Vunipola said.
"I'm not saying we'll beat New Zealand next summer, but playing the best will improve us as a team.
"We're nearly there, we're going the right way, we're going upwards, not standing still.
"We showed against New Zealand that they're a great team, but they are just players.
"They're not average players, they're great players, but they're players just like us and if you put them under enough stress, they will break."
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