And the Hatters, 85 places below the Canaries on the football ladder, went through thanks to substitute Scott Rendell's strike 10-minutes from time.
FA Cup giant-killing stats
Luton's victory was the first time a non-league side has beaten a top-tier team in the FA Cup since Sutton 2-1 win against Coventry in 1989
It also ended a 27-year wait for a non-league team to beat a top flight side away from home
Norwich had not lost to a non-league team in the cup since 1956
It was also the first time since 1949 a non-league side had beaten a top flight side beyond the third round
"I don't normally get that excited on the sidelines," said Buckle. "But the faces of the substitutes and staff was a real picture. It was amazing.
"I watched the players celebrate the goal. I was a little concerned they celebrated too long and would be washed out by the time they got back to the halfway line.
"We knew there would be a response from Norwich and we had to brace ourselves and trust the work we did."
Buckle's previous biggest success as a manager was taking Torquay United out of the Blue Square Bet Premier in 2009 and leading the Gulls to a League Two play-off defeat by Stevenage in 2011.
But becoming the first non-league manager to beat a top-flight side in the Premier League era will now rank alongside those achievements.
"I've been fortunate in a few years of management to have some really good highs. This is right up there. It's an incredible achievement by the players," said the 42-year-old.
"Against Wolves and Norwich there was no fluke about it. We weren't holding on for dear life.
Luton player performs Norwich rap
"After that experience we'd dearly love to play a Premier League club again. This is where everyone wants to be."
Luton striker Stuart Fleetwood believed his side excelled because the pressure was off them against their higher-placed opponents.
He told BBC Radio 5 live:
"We were playing away in front of 26,000 fans but the pressure wasn't on us. When we're at home in the league it is and it was nice to be the underdogs for a change. I think it showed in the way we played.
"The players are buzzing - we are having a couple of beers. But it's back down to Earth on Tuesday night because we're playing at Grimsby in the FA Trophy. So there won't be too much celebrating."
Norwich boss Chris Hughton, however, was left to reflect on the most sobering defeat of his managerial career.
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