Among about 10 former astronauts attending Friday were John Glenn and Armstrong's crew for the 1969 moon landing, Buzz Aldrin and Michael Collins.
"You'll never get a hero, in my view, like Neil Armstrong," said Apollo 8 astronaut Bill Anders, who praised Armstrong after the service for his wisdom and humility in the way he handled becoming a global icon. "It's going to be hard to top."
"America has truly lost a legend," said Eugene Cernan, an Apollo astronaut who is the last man to have walked on the moon.
Sen. Rob Portman (R., Ohio) eulogized Armstrong "as a reluctant hero" and said afterward that 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."
After his space career, Armstrong returned to Ohio, teaching aerospace engineering at the University of Cincinnati and generally avoiding public view for most of the rest of his life.
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.
He said he and his wife were on their honeymoon in Amsterdam, the Netherlands, on the day of the moon landing. He recalled hotel employees bringing champagne to the guests watching Armstrong's first steps together on television, and an Englishman lifting his glass in a toast "to all mankind!"
Taalman's voice cracked as he discussed his visit Friday.
"I just think a really great man has passed, and the world is poorer for it," he said.