Trailing 3-1 after a poor performance in Portugal last week, Bayern needed either a 2-0 win or victory by three goals or more to progress to the semi-finals for the fourth season in succession.
As it transpired, the Bundesliga champions blew their opponents away with five goals in the first half, eventually prevailing 6-1 to seal a 7-4 aggregate success.
"I had the feeling over the last few days that we would do it," said Guardiola, who managed to somehow rip his trousers during the game.
"The players were my heroes after the defeat. Now it's easy to love them."
Goalscorer Thomas Muller added: "It's hard to find any words. I'm quite exhausted, but it couldn't have gone any better.
"We never imagined to play like we played in the first half, it was really hard work. Great compliments to my team."
Robert Lewandowski, who netted twice in the rout, said: "The first half was simply awesome, it was totally great. We are Bayern and we can turn a 3-1 defeat around.
"We knew we had to push really hard. Five goals in the first half are absolutely crazy, of course."
Bayern captain Philipp Lahm said: "We want to win every game. We have a great squad and a big heart, which you could see in the first half.
"You are never safe, but I was quite optimistic for the game. We helped each other and scored at the right time."
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