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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.