The Bayern Munich man has spoken of his desire to help his team win, even if that means not getting goals himself.
The teams meet at the quarterfinal stage of the tournament on Friday, having taken vastly different routes to the knockout stages.
The Germans dominated Group B, winning all three games against the Netherlands, Denmark and Portugal, whereas Greece scraped through Group A, winning just once.
Muller understands that Fernando Santos' side will test his team's patience by defending in numbers against it.
"Greece will defend. We have the reputation of being one of the favorites, so teams tend to play a defensive style against us. We know what we have to do, we will have to be patient, but we will also have to work for our success," he told reporters.
Muller also compared the Euros to the World Cup, saying his side didn't peak in the group stage at either competition, before taking shots at the negative coverage the team has gotten from some of the media.
"We've had tough matches so far, Denmark is a strong team, too," he said. "The level is very high, higher than at a World Cup, but there we didn't play at our best in the group stage as well.
"Everybody in the media is looking for mistakes. Although we have nine points, in front of the goal I sure can do better, however, the media could report a bit more positively. At home all the fans seem to be thrilled by our game, but the media is very critical. Even if we'd win the title, they would be disappointed"
The 22-year-old dismissed suggestions that he should be concerned over having failed to score in the competion thus far.
"As long as I know I've done well it's okay and not that important, but since the world cup the expectations grew a lot. Everyone wants to see me scoring, but I want to help the team," he continued.
"I’m more of an assist-giver. I like scoring goals, but helping the team is more important to me."
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