A Mario Mandzukic hat-trick led the Bundesliga leaders to the comfortable quarter-final win, while Dante and Arjen Robben were also on the scoresheet at the Imtech Arena.
Guardiola said Dante's 26th-minute goal made life easier for his team and is looking forward to a potential finals berth at the Olympic Stadium in Berlin.
"I'm pleased with the performance and it was a great game from us. This is my first go at the DFB Cup," he said.
"Lots of people have told me what a good day out it is in Berlin, and we're only one step away now.
"It's definitely special for me. We had a few problems at the start but it was easier after we scored our second."
Bayern midfielder Bastian Schweinsteiger was similarly impressed by his side and wished Hamburg all the best for the rest of the season.
Bert van Marwijk's men are in the Bundesliga relegation zone, two points behind 15th-placed Freiburg.
"We didn't really know what to expect here. I think we played very well," Schweinsteiger said.
"I hope Hamburg start picking up points very soon. It would be a shame for the club, the city and the people here (if Hamburg were relegated)."
Van Marwijk felt his side were simply outplayed by a team he considers to be the world's best at the moment.
Mandzukic and Dante struck six minutes apart in the first half before two efforts from the Croatian and another from Robben after the break.
"We all saw the team made a decent go of it at the start. Our attitude was right. We tried to close down the space," van Marwijk said.
"But we weren't good enough today to get anywhere against Bayern, currently the best team in the world."
