* Armstrong praised for low-key dedication, heroism
* Service includes bagpiper, Krall singing "Fly Me to the Moon"
* Burial to be at sea on Friday (Adds details, quotes)
By Ian Simpson
WASHINGTON, Sept 13 (Reuters) - U.S. astronaut Neil Armstrong, the first person to set foot on the moon, was praised in a NASA memorial service at the National Cathedral on Thursday as a humble hero who led mankind into space.
Mourners who filled the vast Episcopal cathedral to mark Armstrong's death last month heard him eulogized as a dedicated team player who shunned the limelight for decades after piloting the 1969 Apollo 11 moon landing.
"He embodied all that is good and all that is great about America. Neil, wherever you are, you again have shown us a way to the stars," Eugene Cernan, the last man on the moon as the commander of the 1972 Apollo 17 mission, said in a tribute from the pulpit.
"As you soar through the heavens where even eagles dare not go, you can now truly put out your hand and touch the face of God."
Armstrong, a former Navy flyer and test pilot, died at age 82 following complications from cardiovascular procedures. He is to be buried at sea on Friday at an undisclosed site.
Charles Bolden, the head of the National Aeronautics and Space Administration, said although Armstrong had been the first human to step on the moon, it was his courage and grace under pressure that had made him exceptional.
"We are standing on the shoulders of giants as we get ready to take the next steps into space," said Bolden, a former astronaut.
At the close of the service , Bolden presented Armstrong's wife, Carol, the flag that had flown at half staff over the NASA Johnson Space Center in Houston on Aug. 25, the day he died.
The memorial service included the Navy hymn "Eternal Father Strong To Save" sung by a white-clad Navy choir, a bagpiper playing "Mist Covered Mountains" and a prayer read by Michael Collins, who was part of the Apollo 11 crew with Armstrong and Buzz Aldrin.
Accompanying herself on the piano, Grammy-winning jazz artist Diana Krall also sang the Frank Sinatra standard "Fly Me to the Moon."
"Fly me to the moon, let me swing among those stars, let me see what spring is like, on Jupiter and Mars," Krall sang.
Cernan said Armstrong had always described himself as only the "tip of the arrow" for 400,000 dedicated NASA workers involved in the space program.
As an example of Armstrong's low-key heroism, Cernan told of his response to a man who asked how he had felt when he was landing on the moon with only seconds of fuel remaining.
Armstrong had put a finger to his chin and replied, "'Well, when the gauge says empty we all know there is a gallon or two left over,'" Cernan said, drawing laughter from the audience.
The National Cathedral contains something of a memorial to Armstrong. One of its stained-glass windows, the Space Window, has a piece of moon rock presented by Armstrong, Aldrin and Collins in 1974. (Reporting by Ian Simpson; Editing by Bill Trott)