Sean Reed's Family Says Cop Who Made 'Closed Casket' Jab Should be Fired

The punishment doesn't fit the crime. That's what Sean Reed's family's saying about the cop who got suspended for his "closed casket" joke ... saying he deserved to be fired.

You'll recall the Indianapolis detective got suspended and reassigned after he was heard saying, "I think it's going to be a closed casket, homie" moments after Reed was fatally shot during an incident Reed streamed live on Facebook.

Well, the Reed family's furious over what they essentially say is a slap on the wrist. Sean's uncle, Tyrell Reed, tells TMZ ... he doesn't think the cop received a harsh enough punishment. In fact, Tyrell tells us, "I feel like [the detective] shouldn't be on the force or allowed to be a police officer."

What's more ... Tyrell says the detective's true colors came out with his distasteful joke, because he had no clue Reed's camera was still streaming live. Tyrell adds, "He thought he was doing things in the dark. Now, those words leave a mark on our family forever. I probably don't think his fellow officers appreciated the comment either."

Tyrell says the Reeds have been shaken to their core with the crack made by the detective, whose identity has not been disclosed because of safety concerns. For what it's worth ... Tyrell says things have slowly gotten better over the last few days, thanks to the overwhelming support the family's been receiving from friends and others in the community.

As we first reported ... Tyrell told us it's a terrible enough situation to have one of your family members shot and killed with a camera filming it ... even worse when a cop makes a quip that will be seared into their memories forever.