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Rodrygo pulled one back for the visitors before half-time, but Gabriel Jesus' goal secured qualification for the quarter finals, inflicting in the process a first Champions League knock-out defeat on Merengue coach Zinedine Zidane.
Madrid have won four of the last six editions of Europe's biggest club competition, including three in a row during Zidane's first spell as coach between 2016 and 2018.
But while ex-Barcelona player and boss Guardiola was pleased to get one over on his old Clasico rival, he insisted that winning such ties should be the minimum expected of City.
"It is important, we beat them twice. Zinedine Zidane had never lost a knock-out game," the manager told BT Sport after the final whistle at the Etihad.
"You see the calm and personality they play with, they are good. We are here to try and win the Champions League.
"It is one step, if we think that is enough we will show how small we are. If you want to win you have to beat the big clubs.
"I just spoke with the scouting department about Lyon and they told me to be alert. We have eight days to prepare for it. We will enjoy it and then after we will think about Lyon."
Despite leading on aggregate throughout the second leg City took the game to their more cautious opponents, recording 20 shots to Madrid's nine over the 90 minutes.
The hosts nevertheless benefited from no little good fortune as Raphael Varane erred in both goals, which Pep put down to the effectiveness of his side's pressing game.
"We created a lot of chances and scored two goals with mistakes from them. We tried to convince them to go, go and attack but it is not easy against this team," he added.
"We try to press, sometimes it works and sometimes it doesn't. In general we did a good job.
"We could not expect after 30 minutes be 4-0 up. The second half didn't have much but we created a lot. The players made an incredible effort - all of them.
"The first half we played with our wingers more inside, not wider. I think that was a mistake from my side. We corrected in the second half and were better."