Taking a 2-0 lead into their home leg at the Allianz Arena, Bayern struck first via Bastian Schweinsteiger to open up a three-goal buffer and all but seal their progression.
Lukas Podolski made it 1-1 on the night, striking two minutes later from an acute angle, but it would be the only solace for Arsene Wenger's men, who bowed out at the last 16 stage for a fourth consecutive season.
And Guardiola was critical of the north London club's approach to the second leg, claiming Arsenal sat back despite needing at least two goals from the outset.
"We had a lot of control but the opponent didn't come to push," the Spaniard said.
"It's 2-0 in the head of the players and it's not easy.
"We're 2-0 up and we wanted just to control the game.
"We didn't want to attack too much but we got forward many times and we dominated the game."
Guardiola said he was hoping to quell Arsenal's ability to counter and Bayern did his plan justice as the visitors could not get within a goal of the title-holders.
"We were very intelligent. We wanted to stifle Arsenal's counter-attacks and control the game," he told the club's official website.
"We only allowed them one chance in the first half. All Arsenal did was wait for us to lose the ball. Overall we did very well.
"After they made it 1-1 we had a few problems for 15 minutes but nothing major. We're pleased and everything's good."
Goalscorer Schweinsteiger agreed with his coach that Arsenal lacked offensive vigour.
"We tried to apply pressure and attack. Arsenal pulled everyone back and tried to close down the space," Schweinsteiger said.
"We looked to get at them down the flanks and our penetration was reasonably good. But we failed to score (in the first half).
"For me personally it's great to play 90 minutes in the Champions League against a team as good as this."
