Robshaw became only sixth captain to lead England to a victory over New Zealand and he did so in record fashion with a 38-21 thumping of the world champions.
New Zealand went into the game on the back of a 20-game unbeaten streak while England were harnessing the frustration of narrow defeats to Australia (20-14) and South Africa (16-15).
The message from England all week was that New Zealand were not invincible - but to prove it so emphatically at Twickenham made this one of the great red rose performances.
"International rugby is about results. You can talk about a good performance but today we had to go out there and deliver," Robshaw said.
"We were disappointed not to get the results earlier. It was the best possible response, to beat the current world champions and score the tries we did was something in itself.
"Everyone delivered. Everyone rose to the occasion and proved a few people wrong. All week we were quietly confident.
"No one had given us a chance. People were saying 'what are New Zealand going to beat them by?'
"We were confident in our abilities. Andy Farrell came out in the week and said they were beatable, that there were opportunities for us and we exploited that today.
"We finally got a bit of luck and you need a bit of luck when you play the world champions."
England battled hard for a 15-0 lead which was cut to just a point when the All Blacks hit them with two tries in three minutes after the interval.
At that point, Robshaw brought his men together and they hit back with Brad Barritt, Chris Ashton and Manu Tuilagi all scoring as England ripped the All Blacks apart.
"When they came out and scored two quick tries it was a case of 'come on lads, lets lock this one out'," Robshaw said.
"You get a team that hasn't lost in 20 games, they don't lie down easily.
"We had a word with ourselves, we knew they would start chasing the game."
Tuilagi was England's chief destroyer, playing a key role in all three tries, linking with Barritt for the first before breaking through three tackles and sending Ashton over for his first try in 12 matches.
The Leicester centre then picked off a pass from Kieran Read and galloped nearly 50 metres before touching down, ignoring calls from Mike Brown to go nearer the posts.
"This was very special," Robshaw said. "It was very frustrating the last two games, losing to Australia and South Africa by small margins.
"Getting this win is so good."
Twelve months ago, English rugby was in the gutter after the World Cup but Tuilagi always believed Stuart Lancaster's new-look team were capable of achieving something special like this.
"I believed. All the boys believed," he said.
"We believed we can win against teams like New Zealand, South Africa and Australia. We were very frustrated the last two weeks, to have come so close.
"But the team went back to the hotel after the South Africa game and we kept the faith and it showed it out there.
"I was really enjoying the haka. It was the first time I had faced it. I looked into the eyes of my opposite number and said 'I accept your challenge, now let's play some rugby'."
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