Goals by left-back David Alaba, striker Mario Mandzukic and Dutch winger Arjen Robben sealed a convincing win as the defending champions opened their Group D campaign at Munich's Allianz Arena.
"We played well, we controlled the game with our pressing and I am proud of the players," said Guardiola. "People think it'll be easy for us this year having won the title last season, but that's not how it is."
"We kept the ball well in midfield and we play better when that is the case." After Bayern beat Hanover 2-0 on Saturday, director of sport Matthias Sammer accused Guardiola's team of playing "lacklustre football", but the Spaniard said he had no problem with the comments.
"I speak to Matthias on a daily basis and he has given me a lot of support since my arrival," said Guardiola. "We talk all the time, we talk about the team, we talk tactics, even about the pasta and the fish we had for lunch.
"There's nothing we wouldn't talk about." Austria's Alaba was outstanding throughout, hitting a pin-point free-kick for the opening goal, then playing a deft chip over the Moscow defence for Robben to slam home Bayern's third.
"It felt good to score, it was great to hear the Champions League anthem before the game and know that it's starting again," said Robben. "We have to take things step by step, get through the group stages and take it from there."
After Jupp Heynckes led Bayern to the treble of Bundesliga, German Cup and Champions League last season, Guardiola has been under pressure to continue that success since taking charge in June.
After winning 14 titles in four years at Barcelona -- including the 2009 and 2011 Champions League titles -- the Spaniard has been the centre of much hype since his arrival in Bavaria.
Having changed Bayern's formation, Guardiola has won four of his five Bundesliga games so far, despite missing stars Javi Martinez, Thiago Alcantara and Mario Goetze through injury.
This was arguably Bayern's most polished performance at home this season, even with vice-captain Bastian Schweinsteiger starting on the bench as he recovers from an ankle strain.
Bayern needed just four minutes to get on the scoresheet when Alaba floated a beautiful free-kick over the Moscow wall and out of reach of Moscow goalkeeper Igor Akinfeev.
A second nearly followed on seven minutes when a superb pass from right-back Rafinha landed at Mandzukic's feet with the goal at his mercy, but Akinfeev blocked his shot.
With Bayern dominating possession, the hosts peppered the CSKA goal and it was only a matter of time before the European champions added their second.
Moments after beating Akinfeev with a powerful header which cannoned off the woodwork, Mandzukic was the first onto the end of a Robben free-kick to add the second four minutes from the half-time whistle.
Replays showed three Bayern players were offside, but the relief was palpable on the Munich bench with Guardiola hugging his backroom staff.
CSKA, the Russian league, cup and Super Cup holders, came out fired up for the second-half, but Leonid Slutski's side had only limited opportunities.
The Russians enjoyed a good spell of possession until Bayern added their third when Alaba floated a lovely pass over the defence to give Robben all the time in the world to rifle home.
The Dutchman, who scored the winner at Wembley's final in the 2-1 win over Borussia Dortmund in May, smashed his 68th-minute shot under Akinfeev, who had a busy night in the CSKA goal.
With the outcome decided, Moscow threw more players forward and put more pressure on Bayern's goal, but Germany goalkeeper Manuel Neuer was solid all night.
It was a good start for the champions ahead of their next group stage match at Manchester City on October 2, the same night CSKA host Czech champions Viktoria Pilsen in Moscow.