Dominant Bayern missed a bagful of chances, conceded a last-gasp equaliser and squandered an extra-time spot kick to lose 4-3 on penalties in Munich on Saturday after they repeatedly thought they had done enough to win their fifth European crown.
"It is difficult to find ways to say things to them now," said winger Podolski, who left relegated Cologne after the end of the season to join Arsenal.
"Personally I had to deal with it as well. I was relegated (this year) and you have to live with that. In sports there are ups and downs," he told a news conference in southern France where the team are preparing for the tournament co-hosted by Poland and Ukraine which starts in June.
Bayern's internationals - captain Philipp Lahm, keeper Manuel Neuer, Bastian Schweinsteiger, Thomas Mueller, Holger Badstuber, Jerome Boateng, Toni Kroos and Mario Gomez - will join the team in the coming days.
Mueller said this week that his frustration was growing the more he thought about the game.
"All eight are great players and our quality on the pitch will not be affected by this result," said Poland-born Podolski, who has already amassed 95 caps at the age of 26.
He said processing the defeat should be a matter of days rather than weeks.
"It lasts a few days. The relegation is far more dramatic as there are financial implications and jobs are affected. I dealt with it for two or three days and the same should happen to Bayern and then (they should) start looking into the future again."
Germany, aiming for their first major title since 1996 and their fourth European trophy, take on Portugal, Netherlands and Denmark in the group stage of the tournament.
"The last few tournaments we were happy with semi-final finishes but we are that good now and have developed well in the past few years to be able to say that we will challenge for the title," said Podolski.
Germany were runners-up at Euro 2008 and clinched third place at the 2006 and 2010 World Cups.
"It is good to be able to say 'We want the title'. If we get off to a good start against Portugal then that will be perfect. We need to be on fire in that first game and the pitch needs to light up," he said.