The City manager, who had been calling for a strong response following a sluggish start to the Premier League campaign, said he was delighted for both his players and the supporters.
The win was powered by Erling Haaland, who struck twice to underline his lethal touch in front of goal. Phil Foden and Jeremy Doku also starred, tormenting United's defence and ensuring City maintained control from start to finish.
Guardiola admitted he had expected such a performance, but the manner in which his team delivered exceeded even his own demands.
For City, the result was more than just local bragging rights. It represented a crucial step in re-establishing rhythm after early-season stumbles, while also providing the perfect boost before a return to European competition.
"We want to be close enough in February and March to fight for the title but this period was important.
"Our players have a lot of pride and they wanted to try to do better on a special day.
"Our walk in front of the fans to see them so happy, our job is such a privilege.
"We have many things to improve. We are not a team but step-by-step the victories help a lot."
Next up is a UEFA Champions League clash with Napoli, where City will encounter a familiar face. Kevin De Bruyne, their "old pal" and a former midfield linchpin at the Etihad, is now part of the Italian champions' squad.