The USWNT saw a 44-match unbeaten record end in humbling style as the tournament favorite and world No. 1-ranked side was undone by two Stina Blackstenius goals and one from Lina Hurtig.
With four gold medals, the United States has more than any other nation and is vying to become the first team to win Olympic gold following a World Cup title.
To do that, though, the team must move on quickly after the loss to Peter Gerhardsson's side. Speaking after the match, Rapinoe said: "We got our asses kicked, didn't we? ... I thought we were a little tight, a little nervous, just doing dumb stuff.
"There's no time to dwell and think about if Sweden is living in our heads or not. We've got another game in three days."
Rapinoe, who came on in the 64th minute with the score 2-0, added: "Did we expect this result tonight? No.
"It's frustrating, and it's frustrating that it's Sweden. They found a lot of space on us. I don't even know how many goals we have given up this whole year. I don't remember the last time we gave up a goal. So to give up three is not great."
Sweden, ranked No. 5, has been the U.S. team's nemesis of sorts in recent years. The Swedes bounced the Americans from the 2016 Rio de Janeiro Games in the quarterfinals, their earliest U.S. Olympic exit ever, by making a defensive stand.
In April, Sweden played the United States to a 1-1 draw in Stockholm, which snapped a winning streak dating back to January 2019 when the Americans lost to France in the runup to the World Cup. It was the U.S. team's only draw this year.
U.S. coach Vlatko Andonovski said: "It's obvious we put ourselves in a big hole, but we're the only ones who can get ourselves out of it.
"It's not going to be easy. We've got to get positive results in the next two games, but the fact there is still a chance [means] I know this team is not going to give up."
Sweden leads Group G heading into Saturday's game against Australia in Saitama, while the United States faces New Zealand. The top two teams in the group advance to the knockout round.
"We have very brave players and very good leaders," Gerhardsson said. "Brave attitude to win the ball and transition so well. Yeah, I'm satisfied."
In 2008, the United States also lost its first match (2-0 to Norway), but went on to win the gold medal.
"I think ultimately as an athlete you go through ups and downs, and this is a hard result, but it's the nature of a tough tournament," U.S. forward Christen Press said. "It wasn't going to be easy. We weren't going to breeze through six games no matter what. So here we are."
Information from The Associated Press was used in this report.