"This was the year of firsts: first holidays, first birthdays, first everythings without mom, without grandma," Melissa wrote.
The new Fashion Police host, 47, has a 14-year-old son, Cooper, who was very close to his grandmother.
"While it's been difficult, I've been amazed by the outpouring of love and overwhelming kindness we've received from family, friends and people whose lives were touched by the woman they knew as Joan - a woman we all miss so very much," Melissa wrote.
"Everyone expects me to have this big grand plan for the 4th and I am just going to be spending it with my son," she said. "He is going to go to school, I am going to go to work and come home and light a candle, and have a glass of wine."
Earlier this week, Melissa shared that she and Cooper scattered some of Joan's ashes in Wyoming during their annual family vacation to the Great Plains state.
"Cooper and I talk a lot about what would be the best way to honor her legacy, and the best way to honor her legacy is to be okay," Melissa said.
For Joy Behar, the loss of her friend still hasn't fully set in yet.
"I can't believe she's dead," she told ET. "She was such a force of nature, Joan. You can't tell me she's not on this planet anymore."
Melissa sat down for her first episode of Fashion Police last month, where the panel took on the wild and sexy styles at the MTV VMAs. Watch the video below to see her channel her late mom for the E! show.