The actress is thought to have drowned while swimming in California's Lake Piru last Wednesday, and an extensive search of the area involving more than 100 specialists has yet to locate her.
Upset fans have questioned why some of Rivera's co-stars have not publicly commented on her disappearance, with the heavily-pregnant Lea Michele - already under fire for allegations over her behind-the-scenes behaviour - being forced to delete her Twitter account over the weekend after receiving abuse.
Making her first post on Rivera's disappearance, Riley - aka Mercedes Jones - wrote: "Show some respect. All our energy is going toward helping find Naya and praying for her safe return and for her family. No one owes anyone online a performance of grief.
"This is very real and devastating. Focus on Naya and her family. Not us. We don't matter right now."
Kevin McHale, who played Artie, retweeted Riley's message and added: "I cannot begin to understand what Naya's family must be feeling. I know the rest of us are completely shattered, but not without hope.
"Please respect her family & their privacy in this moment. Please refrain from judging those who don't show their pain on social media."
"I have spoken to Sheriff Eric Buschow and rest assured they are using every single one of their resources to locate our Naya," she wrote. "I have full confidence that they're doing everything they can, and probably more.
"We will hold off on the citizen search and rescue until we get the go-ahead that they'll allow volunteers. Understand it's 110 degrees here and if you're not highly trained in search and rescue, this could end up a much more dangerous situation for everybody involved.
"Please be kind, compassionate and caring for those who are looking for our Naya."
The search will enter its sixth day later on today.