On Earth, at some times and places, we can see many stars in the sky. When I watch rocket launch videos, or look at NASA imagery from the Apollo missions, I rarely see any stars. Why is this? The stars are obviously there, why can't they be seen in these circumstances?
Aperture. The aperture diameter is too small and frame rate too great to capture dim distant sources of light. It's really that simple. Consider how the rocket's engine, its ejecta and the illuminated Earth in the background would look if the camera's aperture was set to detect background stars. Any foreground lit object would cause frame overexposure and everything would appear white, possibly even cause permanent sensor damage if it caught a ray of light from the Sun.
You can try this at home with any point and shoot camera. Point it towards a full moon (or close to being full) during night, set it on auto-exposure, and then see if it also caught any stars appearing around the Moon. It won't. Even the Moon at night is too bright and capturing stars requires larger aperture, longer exposure and/or greater sensor sensitivity. You might succeed in capturing Venus (apparent magnitude of up to −4.89) when it's particularly bright next to a half or less lit Moon, but that's not a star. Brightest star on the night sky, as seen from Earth or indeed anywhere near our Solar system, if we exclude the Sun itself, is Sirius at mag. −1.46 (23.55 times dimmer than Venus at its brightest, and over 38,000 times dimmer than full moon at apparent magnitude of −12.92).