The new Arsenal signing believes 'Die Mannschaft' were rewarded for their determined efforts against their Group B opponents, and is looking ahead to the game with the Netherlands
Joachim Low's side only managed one serious attempt on goal in the first 45 minutes, but Mario Gomez's header in the second-half was enough to give them all three points.
After being lauded for their attacking flair in the 2010 World Cup in South Africa, Germany were expected to continue that form into the European Championship, but Podolski says that victory is what counts.
"The three points are important," he told Goal.com after the game. "Maybe we did not play as well as in 2010, but we fought hard and in the end it was important to start off with a victory.
"If you look at the Portuguese [team] you cannot say that they're bad opponents. We have room to improve but the victory was very important, especially after Netherlands surprisingly lost against Denmark.
"Portugal had two good attacks at the end. We had little space, even after the [goal that made it] 1-0. We did not play as well offensively as in 2010. We need to improve that.
"Everybody expects 'fun football' and attacking football from us. We have to match those expectations."
Now, the new Arsenal signing is switching his focus to die Mannschaft's next fixture, when they face Oranje in Kharkiv on Wednesday.
"It won't be easier against Netherlands. They have their backs against the wall. If they lose, they are out. We can qualify for the quarter-finals."
Podolski also feels that the Germans' 3-0 success when the two sides met in a friendly last November will give them the confidence to go up against the Dutch again.
"The 3-0 win back in November is still a topic in their team, maybe. It's the same team that will be on the pitch for them. We don't have to hide."
Germany and Netherlands kick off at 20:45CET on Wednesday.