The service opened with bagpipers, who led Armstrong's relatives in a procession through the packed church, followed by a US Navy honor guard for Armstrong, who was a Navy pilot before joining the space program.
A recording of an excerpt of then-president John F. Kennedy's famous speech, given 50 years ago Wednesday, reminded mourners that the US pledged to go to the moon and commit to other accomplishments to win the Cold War space race "not because they are easy, but because they are hard."
Armstrong took the "first small step on a world beyond our own, but it was the courage, grace and humility he displayed throughout his life that lifted him above the stars," NASA chief Charles Bolden said of the astronaut, who died on August 25 at the age of 82.
"America's leadership in space, and the confidence we can go farther into the unknown, rests with the achievements of Neil and the brave men with which he served," he continued.
"No one, but no one, could have accepted the responsibility of his remarkable accomplishment with more dignity and more grace than Neil Armstrong," said Eugene Cernan, the last man to walk on the moon.
Cernan, who called Armstrong a good friend, said the Ohio native never wanted to own the accomplishment.
"It was never about Neil -- it was about you, your mothers and fathers, your grandparents, about those of a generation ago who gave Neil the opportunity to call the moon his home," he said.
The grainy black-and-white broadcast of Armstrong's July 20, 1969 moon walk was seen by an estimated half a billion people.
"That's one small step for man, one giant leap for mankind," they heard Armstrong say, though he later claimed that an "a" before the word "man" had been lost in transmission.
Armstrong, who grew up in rural Ohio, was decorated by 17 countries and received a slew of US honors, but was never comfortable with his fame and shied away from the limelight.
The public memorial came two weeks after a small, invitation-only funeral, held on August 31, that reflected Armstrong's intensely private nature.
The Apollo 11 commander, who died of complications from cardiovascular surgery, will be buried at sea.