The 38-21 victory was England's first triumph over the All Blacks in nine years.
"People had written us off," Robshaw said on Sky Sports 1.
"That fuelled the fire. Everyone ran out there and believed we could do it."
He added: "We had a bit of luck. We had the bounce of the ball but to beat the world champions you need a bit of that."
England flanker Tom Wood said: "This is an absolutely brilliant day. We put our hearts and souls into that."
New Zealand captain Richie McCaw was gracious in defeat.
"England played particularly well and credit to them," he said.
England coach Stuart Lancaster was pleased with the "balance and intensity" of the team.
When asked what had pleased him, he said: "The way we mixed up our game. The scrum was good. The defence was outstanding."
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