Similarly, the astronauts eyes are adapted to the daylight scenes around them so they didn't see stars in the sky either. As an experiment to verify this affect, go from a brightly lit room to a dark location just outside and see if you see any stars when you first look up at the sky. Stars were seen, however, when the conditions were right and the crew was dark adapted.

Another interesting remark from Edward Lu:
It is fun to watch stars as they rise or set through the atmosphere as we circle the Earth. They start to twinkle as the light rays bend while passing through the uneven density of the atmosphere. Then, as they get closer to the actual horizon, they start to look orange and then red before blinking out. Sometimes they even turn green briefly.

Why didn't any of the 21 Apollo astronauts talk about the stars?

That anonymous person also sent me links to several sites that have photographs taken by the astronauts. The image below is a portion of one of the photos taken by Don Pettit from a window in the space station. Note that stars are everywhere. You can find this and other photos at this NASA page.

"Flying the U-2 is real interesting. Unlike flying down lower in the atmosphere like most airplanes, some of the visual sights you see up there are incredible. In daytime, the sky looks a lot different up there. Above all the haze and everything in the atmosphere, the sky is a lot darker, almost purple. It is really an amazing sight. Every once in a while during a mission, you just have to stop and really take a look around and appreciate what you've got up there.

"Night time is a little different also. The air is so much clearer up there; you can see what seems to be 10 times more stars. They just carpet the sky.

Although stars would not normally be visible to the naked eye during daylight, whether from the Earth, the Moon, or on orbit, the planet Venus (which is much brighter than any of the stars) was actually recorded on film by astronaut Alan Shepard at the conclusion of his second extravehicular activity, during the Apollo 14 mission. Shepard was preparing to ascend the ladder to re-enter the lunar module Antares, when he likely noticed Venus shining brightly next to the crescent Earth. He made a series of photographs with his chest-mounted Hasselblad camera, likely all at 1/250th second exposure, and differing f-stops. Owing to its position closer to the Sun and its complete coverage by clouds, Venus has a higher surface brightness than Earth, and is indeed visible to the unaided eye in broad daylight from Earth, given a sufficiently transparent sky. It would have been plainly visible to Shepard in the lunar sky, and easily recorded on film. For a complete explanation, consult the "Images" section of the Apollo 14 Lunar Surface Journal.[5]
In the Apollo 11 press conference, Neil Armstrong states that he was "never able to see stars from the lunar surface or on the daylight side of the moon by eye" [6] Stars were visible with the naked eye only when they were in the shadow of the Moon. All of the landings were in daylight.[7]