City won 3-1, meaning they reached the quarterfinals 6-2 on aggregate. Erling Haaland, Manuel Akanji and Julian Alvarez struck for the hosts.
Guardiola said: "We're into the next round. Still we are there in this competition. It was difficult to attack them (FC Copenhagen) because they are well organised playing four or five at the back.
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"We are well respected for our openness. Before I arrived we didn't believe we could do it. It's a question of time, a process. They (hierarchy) gave me time, gave us time.
"We are a team that believes we can do it. Listen, we're competing with Real Madrid and Bayern Munich. We don't know who we are going to face. It's a question of wait and see.
"The important thing is seven years in a row we are here."