Was the white paint a latex? If so, you might try using Goof Off or Afta. Don't pour it directly on the carpet. Use a WHITE rag. (Other colors might bleed and make your mess worse.) Put a bit of Goof Off on the rag and start dabbing your stain. Don't rub back and forth, just blot.

Depending on the carpeting, any chemical might take the rose color out. But I propose you don't have much to lose at this point.