City won 2-1 at the Etihad to reach the quarterfinals 4-2 on aggregate.
Guardiola's side will now face Lyon in the one-game knockout format in Lisbon after inflicting Zinedine Zidane's first elimination from the Champions League, the French manager having won it three times in his three previous seasons in charge.
It was a victory City fully merited as their intense pressing game forced Real into numerous mistakes, with France World Cup-winning defender Raphael Varane in particular unable to cope with the pressing of Gabriel Jesus.
City, though, created the better opportunities in an excellent performance - whereas Real missed the leadership and nous of central defender Sergio Ramos, who was suspended after being sent off in the first leg.
Without Ramos alongside him, the uncomfortable Varane made another error when his headed back-pass fell short of Thibaut Courtois to allow the lurking Jesus to pounce in the game's decisive moment after 68 minutes.
Guardiola declared: "More than satisfied. The players will go to Portugal to try to make the next step.We know exactly what team we beat.
"First half our wingers were more inside than outside and it was not good. Second half they played wider and it was better. It was a wrong decision I had done.
"This competition punishes you, we know that from our own experiences. Jesus was the man of the two games for us, he set up the first and scored the second.
"We more than deserve to be in the next stage."