Shane Monahan touched down twice and Jonny May, Charlie Sharples and Ben Morgan also crossed as Gloucester piped Cardiff Blues of Pool 2 to the final place in the last eight courtesy of a higher number of tries scored across all six pool games.
"It's an exceptional result for us. The last time we won an away game in France in the Heineken Cup was the 2007/08 season. Not many sides come away with a win here but we've managed it with a bonus point," said Davies, who believes playing European knockout rugby will have a huge effect on his players.
"To a man, the players stood up individually and performed. We backed ourselves to play rugby and have a go at Perpignan. There were a couple of areas where we were second best in the first half but we put that right in the second. The boys knew what was in front of them and overall it was a very good performance.
"To be in a quarter-final in Europe in is big for us. The more exposure we get at this level the better. It will be a great occasion for us and it will be a great thing in terms of the development of this team. The more experience you gain, that's when you start to move forward and win these big matches.
"We've started going in the right direction. We got knocked backwards but Munster was a step forwards and today was yet another."
Gloucester's continental campaign looked all but over after a shock home defeat to Edinburgh was followed by another Kingsholm reverse to pool winners Munster last week. But the 2006 Amlin Challenge Cup winners bounced back in brilliant fashion to grab the bonus point win they needed to keep their European dream alive.
May was the man who set them on their way at the Stade Aime Giral as he sliced through four defenders from fully 80 metres after picking up a loose ball on the edge of his own 22, with his pace and balance leaving the cover grabbing at thin air with 13 minutes on the clock.
"He's got those moments in him and every team needs players like that, players who can finish a half chance or create something from nothing," added Davies.
"We knew if we could turn them over we could cause them problems and he's a superb finisher."