Your question is a very interesting one. Most children get angry and tantrum when their parents say no. This is because they sense that their angry resistance might make you change your no to a yes. Both of your children react with sadness. This makes me wonder if they have gotten either too many nos, or a bit of a harsh delivery of your no.
It’s really important, dear Mom, that you first ponder this query openly and honestly. It will save you a lot of heartache down the road. The second thing you need to do is work on accepting your children’s feelings, warts and all. Your question/comment, “How do I change this behavior and quickly?” tells me it’s uncomfortable for you when this kids get sad, whine, cry, break into displays of powerful emotions. Your discomfort might be giving the kids a feeling non-acceptance.
Children (and adults) all want the same thing: to be loved and accepted flaws and all! Try setting your limits by reflecting out loud empathically that you see how much your child wants to (fill in the blank with the desired activity), then continue by expressing permission for her to feel sad and angry at Mom for saying no. Then, be sure to let her know when she can do the desired activity to give her hope. Turn your frown upside down and hers will follow!