Having drawn 0-0 in the first leg, Bayern took full advantage after Olexandr Kucher was shown the quickest red card in Champions League history in the third minute, conceding a penalty for a foul on Mario Gotze.
Thomas Muller duly slotted home the first of his two goals, with Jerome Boateng, Franck Ribery, Holger Badstuber, Robert Lewandowski and Gotze also netting for a ruthless Bayern side.
"Of course we are satisfied. It was a clear result," Guardiola said. "It was little easier as we were playing 11 against 10 for a long time. They did not have one really good chance.
"Congratulations to my team. We will play in the quarter-finals, that is what we expected and what we wanted. It was first time in my career that we were playing with five forwards.
"In the first leg game. we had lots of problems with their defence, so today I decided to play with Ribery and [Arjen] Robben in the middle and Lewandowski and Muller.
"We were dominating the game. Shakhtar has really great quality especially in the offence. I knew that. But of course it became a little bit easier because we played with one more player."
Meanwhile, Robben allayed fears over the trapped nerve that forced him off after 19 minutes.
He told Voetbal International: "It's nothing serious, it was a bit unlucky. At the start I flew with everything I had to the goal to slide the ball in.
"I probably did block my back and pinch a nerve. In a few days I will be back. The muscle is okay."
