The Bavarians came under intense criticism from director of sport Matthias Sammer at the weekend, claiming the players were playing without emotion and hiding behind their new coach.
There was little sign of that in a blistering opening as David Alaba smashed in a free-kick after just three minutes as they laid siege to the CSKA goal.
Bayern deservedly doubled their lead just before half-time, Mario Mandzukic heading home an Arjen Robben free-kick, before the Holland winger scored the third after the interval.
"We played well, especially in the first half," Guardiola said.
"I'm very, very pleased, and very proud about this performance. The first match after you've won the Champions League is never easy.
"Everyone thinks it'll be simple, but it's never easy at this level."
The performance also drew praise from Bayern chief executive Karl-Heinz Rummenigge, who suggested the backroom staff fully supported the players despite Sammer's comments.
"This team has real quality, and we have complete faith in the players," Rummenigge said.
"We know they're always capable of a performance like this. They've picked up where they left off in London against Dortmund (in last year's final) with a top-class performance."
Sammer is due to meet Uli Hoeness later this week after the Bayern president publicly reprimanded him for his statements.
While those comments have brought scorn Robben admitted Tuesday night's win - achieved without injured trio Bastian Schweinsteiger, Mario Gotze and Javi Martinez - had been a vast improvement on the 2-0 win over Hannover at the weekend, which provoked Sammer's outburst.
"It felt good again today," he said.
"There was a difference today compared to Saturday. We played well today, but we have to keep our feet on the ground.
"CSKA were good opponents, so winning 3-0 is a good start. The first task is to survive the group stage, and then we'll take it as it comes.
"We're in a process of development and we can still get better. But we'll take it on from here."
CSKA coach Leonid Slutski admitted his Russian champions had been outplayed.
"Our opponents were very strong and took all their chances," he said.
"They were one step ahead of us throughout the match. We conceded the first goal much too early, it caused us a lot of problems and dictated the course of the match.
"After that, we didn't create many chances on the break, but we made very few openings in any case."