Britney made the sad announcement Saturday, saying ... "We are grateful for what we have in the process of expanding our beautiful family 💝 Thank you for your support." She goes on to explain that she and Sam Asghari lost their miracle baby early in the pregnancy.

BS also says they're going to try again, and asks for privacy as well.

Five weeks ago the singer had posted a confusing story about losing weight, then gaining it back ... then taking a pregnancy test and ultimately declaring, "I am having a baby."

She'd posted a slew of nude photos in the last week, but Britney said they were all from "before there was a child inside me" -- explaining why she didn't have a baby bump in any of the shots.

Brit and Sam were in Cancun earlier this week, seemingly trying to enjoy themselves while doing some jet skiing.

Last summer, Britney famously testified, during a conservatorship hearing, she wanted to have a baby with Sam -- and since the conservatorship ended she's posted several times about having baby fever.