Sen. Rob Portman, an Ohio Republican, eulogized Armstrong "as a reluctant hero" and said afterward the service was a mix of emotion and humor, with Armstrong's two sons talking about him as a father and grandfather.
"He touched the lives of so many," Portman said.
"He was the embodiment of everything this nation is all about," said NASA Administrator Charles Bolden. Armstrong, he said, had a courageous drive for exploration while being an "incredibly humble" man who probably wouldn't have wanted all the attention of Friday's service.
It included a Navy ceremonial guard, a bagpiper corps and songs including "When the Saints Go Marching In." Four Navy fighter planes flew over at the end of the service, one flying upward in tribute to Armstrong, a former Navy pilot who flew combat missions in Korea.
Raised in Wapakoneta, Ohio, Armstrong developed an early love for aviation.
He commanded the Gemini 8 mission in 1966 and Apollo 11's historic moon landing on July 20, 1969. As a worldwide audience watched on TV, Armstrong took the step on the lunar surface he called "one giant leap for mankind."
Juri Taalman, 78, said he made a special trip from Hartford, Conn., just to stand across the road from the club where the service was held, in tribute to Armstrong.