David Villa bagged the third and decisive goal for the Spanish side after two goals from the majestic Lionel Messi. Jordi Alba made a crucial defensive stop on Robinho on one end and then wrapped up the victory in stoppage time.
"We were lucky to score early and that helped us a lot," Pique told reporters. "The atmosphere was amazing, the fans know we need them and for them we played well.
"We were better than Milan from the start tonight, and fortunately we managed to score the goals to qualify."
Villa then spoke of the confidence flowing through the Barca team after such a heroic victory, as the Catalan side overturned Milan's two-goal edge from the first leg and kept a clean sheet.
"The fans were always behind us, they always trusted us," Villa added. "They knew we could do it and in the end we did it for them. When you go through a night like this all of the bad days are forgotten.
"After experiencing what we did tonight we don't care who we get in the quarterfinals."
Alba echoed Villa's thoughts, believing that a continuation of the club's intensity and form is vital to its fight toward European glory.
"This was a very important victory for us," Alba told reporters. "We were very good defensively and going forward. We knew exactly how to play this game tonight.
"We will look to continue with the same intensity in the next round."