Brooke Williams spoke passionately about the injustice she said her uncle received when he was killed on 25 May after police officer Derek Chauvin placed his knee on the man's neck for eight minutes and 46 seconds in Minneapolis, Minnesota.
Her question echoed
Donald Trump's campaign slogan - make America great again - although she did not name the president.
At the service in Houston, Texas, Ms Williams, referencing her uncle's final words, said: "I can breathe and as long as I can breathe justice will be served.
"He always moved people with his words. The officer showed no remorse for watching my uncle's soul leave his body.
"He begged and pleaded for you to just get up.
"Why must this system be corrupt and broken? Laws were put in place for the African-American system to fail. These laws need to be changed. No more hate crimes, please.
"Someone said make America great again. When has America ever been great?"
Speaking at the private funeral that was broadcast live, she called Mr Floyd's death "not just a murder, this is a hate crime".
"America, it is time for a change, even if it begins with protests, no justice no peace," Ms Williams added.
"My brother and mum tells me this all the time - God says high, he lives low. Thank you Houston, he's always loving the hometown."
Ms Williams spoke after Mr Floyd's brother broke down in tears remembering his sibling, and after others spoke about their time at school with him in Houston, most memorably for his basketball skills.
While Mr Floyd died in Minneapolis, he only lived there for a few years and grew up in Houston where he will be laid to rest next to his mother's grave.
