Bayern began the defence of their European crown in some style as goals from David Alaba, Mario Mandzukic and Arjen Robben saw them sweep aside their Russian counterparts comfortably.
Leonid Slutsky's men struggled to cope with Bayern's dynamic frontline, leaving Guardiola delighted.
He said: "I'm very satisfied with the performance, especially our first-half display. The first game after winning the Champions League is never easy.
"Everyone always thinks it is, but it’s not. The style we play is Bayern's style, not mine. I'm here to support my new players and I'm very, very proud of them today."
The victory gave Bayern the best possible start to their Group D campaign, although goalscorer Robben was quick to highlight the importance of remaining focused with tougher tests to come.
"We need to stay calm and not get ahead of ourselves," he said. "We are taking the competition step by step and today was a good start, nothing more.
"We know that getting through the group stage is the first objective. It is still early days."
Alaba was also happy to pick up a win on matchday one, but he echoed Robben's sentiments.
He said: "We are pleased to win, but we have to continue working on our performances and try to deliver what our manager asks of us."
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