In the latest episode of The Michelle Obama Podcast, the 56-year-old said her “community wouldn’t have accepted” the approach taken by Mr Trump, who denounced protests sparked by the police killing of George Floyd, an unarmed black man, in May.
In a discussion that spanned race, families and parenting, the former first lady said "almost everybody" she knows has suffered from being accused of wrongdoings because they were Black.
"So you've got to be better than, you've got to be 10-times better than," she told listeners.
"When we were in the White House, we could've never gotten away with some of the stuff that's going on now, not because of the public, but our community wouldn't have accepted that. You worked, you did your best every day. You showed up," Ms Obama said.
Recalling the moment her brother, Craig Robinson, was stopped by police when they were children, she added that Black children are still taught from a young age that others will assume the worst in them because of their race.
"You were riding down the street and you got stopped by the police, and they accused you of stealing your own bike," she said of her brother. "And they would not believe you, to the point where you were like, 'Take me to my home.'"
Mr Robinson, said the incident was "terrifying" and left him "heartbroken," because he was "always taught that the police are your friends ... and they'll believe the truth."
"What a lot of folks who are not in our position don't understand is that this is such a way of life when it comes to interacting with the rest of the world," Ms Obama said. "It doesn't matter who you are and what kind of values you have, nobody thinks about the fact that we all come from good families that are trying to teach values."
"When you leave the safety of your home and go out into the street, where being Black is a crime in and of itself, we have all had to learn how to operate outside of our homes with a level of caution and fear, because you never know," she added.
Ms Obama did not mention the US president’s name during the podcast, whilst offering remarks on the current situation.