The OP said her daughter doesn't care about winning. She just want to be part of the group that's in the center of attention. She need to learn that's not possible all the time and how to handle it without putting down others. She's a child, which makes it easier to slowly teach empathy now rather than later. Children will hit out or pout or throw tantrums, but those are teachable moments as they happen (or when they calm down).
I'm glad the OP is at least recognizing it does more harm than good in the long run to put down other children to make her daughter feel better and hopefully stop.