An own goal by Jan Vertonghen and a Simeon Jackson winner - after Gareth Bale had fired Tottenham ahead - earned the Canaries a famous win, with Clint Dempsey also missing a penalty for the visitors in the closing minutes of the match at Carrow Road.
Bunn was making only his second start of the season and Norwich boss Hughton said: "I thought he was excellent.
"He is a really good goalkeeper. I can't imagine he was at fault with Tottenham's goal because it was a wonderful strike from Gareth Bale.
"Overall he showed good composure and he had good hands. The save for the penalty was fantastic. He was brave."
Hughton also felt the penalty kick should not have been awarded when Kyle Walker appeared to fall over Marc Tierney's out-stretched foot.
He added: "I thought Walker certainly made a meal of it. Marc said he didn't touch him. On the angle I have seen you can't tell if there is any contact.
"But it's a nice feeling to win. Spurs are a fantastic team that will have a good season so to beat a team of their quality is a real nice feeling."