Despite being at home for the second leg, the Perth side were under pressure for much of the night but they managed to secure a second 1-1 draw.
Stevie May's first-half spot-kick put the hosts in front but Marco Schneuwly levelled and there were no further goals in extra-time.
And home keeper Alan Mannus then denied Schneuwly in the subsequent penalties, leaving Tam Scobbie to give Saints a 5-4 shoot-out win and set up a third qualifying round tie against Slovakia's Spartak Trnava next week.
Wright said: "I can't come up with the accolades for what the players have achieved.
"But for us to beat the likes of Rosenborg and Luzern two years running is fairy-tale stuff.
"It shouldn't happen, really. But it does, through a determination, a spirit, a togetherness, organisation, a wee bit of luck at times, and a wee bit of quality at times. It proves what they can do.
"The game's all about those players in the dressing room. I can't thank them enough and I'm sure the fans will be thinking the same as well.
"There's no doubt Luzern created more chances, put us under more pressure, and controlled large parts of the game, but we got our noses in front.
"It doesn't make up for last year (an agonising penalties loss to FC Minsk), because we should have won then.
"But what it does is give us a chance to progress again. I haven't seen the Slovakian side but I would be surprised if they were better then Luzern."
Luzern head coach Carlos Bernegger said: "I am disappointed. We started well and created chances but could not get the goal we wanted.
"It's not clear whether it was a penalty for St Johnstone but, if they were awarded a penalty, then we should have also had one in the second half.
"In the end, St Johnstone were luckier than Luzern and we wish them luck in the next round. For us, we have to concentrate on our league."