An early own goal from Eric Bailly and a Bernardo Silva effort proved enough for the champions on Saturday but their margin of victory in a one-sided Premier League encounter could have been even more emphatic.
City were thwarted a number of times in the first half by United goalkeeper David De Gea while the hosts struggled to create meaningful chances throughout.
City manager Guardiola said: “Huge credit and my admiration again – and pride – to these players for the commitment and the fact that we played a really good game from the beginning until the end, except the first 10 minutes of the second half when we missed some stupid balls.
“The best way to silence Old Trafford is to have the ball with a lot of passes and attack the box in the right moments and we did that. We played a really good game.”
Despite all their recent success, City had not won any of their four previous derbies in the Premier League.
Guardiola, however, did not wish to be drawn on suggestions the convincing nature of City’s victory had firmly re-established them as the dominant force in Manchester.
He said: “For our fans Manchester City is the best club in Manchester and for red fans United is the best club.
“All we can say is we have done really well, winning a lot of titles and being up there all the time. I see how proud we are and how hard we can run.”
United began with three centre-backs in the hope of absorbing City pressure and hitting back on the counter-attack.
Guardiola insisted their plan did not overly concern him as he focused on his own side.
He said: “Let me be gentle – I never analyse or judge what the opponents do or what they have done.
“The (derby) games in previous seasons have been quite similar. They wait behind and use one mistake to punish us on the counter-attack.
“They didn’t control the games but they waited, maybe because they respect us and that’s a big compliment to us. We did our game.”
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