Switzerland have been tipped to reach the last 16 from the group along with hosts France, but Albania and Romania stand in their way.
"Of course, journalists talk about it, of course I'm a player who can make a difference in this team, but for me it's not important to be the star in the media, I'm just playing for the squad," Shaqiri told a news conference on Friday.
"I'll be fighting for the squad. I will try to make a difference but Switzerland do not depend on one player.
"We have always stood out as a team so we will stay as a team."
It will be a special game for Shaqiri, whose parents are Kosovar Albanian.
"Tomorrow will be a serious game, both teams will give their best to win it, there won't be any friends," he said.
Captain Stephan Lichtsteiner insisted the Albania match could be key.
"For everyone it seems to be done and dusted, France first and Switzerland second. It's not that easy so the most important thing is to win tomorrow's game," he said.
France take on Romania in the tournament's opener later on Friday.
(Reporting by Julien Pretot; Editing by Toby Davis)
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