Goals from Toni Kroos, Thomas Muller and Mario Mandzukic have put the Bavarians firmly in control of the Champions League last-16 tie, with the return leg to be played at the Allianz Arena in two weeks' time.
"The result speaks volumes," UEFA.com quotes Podolski, who scored the Gunners' goal, as saying.
"Bayern had a lot of pressure in the first half. However, we came out well in the second half and pulling one back was deserved.
"It will now be very difficult for us away from home."
Arsenal went out at this stage of last year's competition to AC Milan.