Michael Jace -- Dead Wife's Family Seeks Money -- We Need Help Burying April

The family of Michael Jace's dead wife April say they can't afford her funeral, and the future cost of caring for her kids -- and they're turning to the public for help ... TMZ has learned.

April's family set up a GoFundMe account on Thursday ... with a message thanking the public: "Many of you have generously asked how you can help the family as we grieve and navigate the aftermath of this tragedy."

They've received nearly $13K from 187 people already. We're told they're trying to raise at least $20K -- for funeral expenses and to care for April's sons ... ages 5, 8 and 18.

Jace was charged Thursday with April's murder.