Have you regretted putting your mom or dad in an old age nursing home?

Not if they get care. If you can't provide for their care yourself, a care center is the next best option. Make sure that they get good care there. Visit them often, and if you are able take them out on pass and let them go places and do other things. You should not feel regret if you know they are receiving good care and stay active with activities.
People often do. People often regret putting their parent into a nursing home. But you have to realize that the choice is not an expression of lessening love for the parent. Rather, it's an acknowledgment of the improved medical care, physical strengthening and well-being that the parent can achieve in that setting, so ultimately it's another expression of that great love you have for your parent.