As long as they ae not diseased putting them back where they came from, your soil, will put the nutrients they contain back into that soil, and that is good. You could take them from the garden to the compost pile and then bring the compost back to the garden, but this way saves many steps.

Great! Thank you for that confirmation. My roses have been producing lots of flowers, and I have been putting the spent blossoms on the bed around the plants.