The Independent Police Complaints Commission (IPCC) found he had not swallowed a controlled substance before dying in police custody.
Diane Abbott said urgent work must be done to rebuild trust between police and the local community.
Mr Charles' death led to protests, including one which turned violent.
The Hackney North and Stoke Newington Labour MP said the violent demonstrations were "wrong" and she has joined with Mr Charles' family in calling for peace.
Figures released on Tuesday showed a "disproportionate" use of force against minority groups by the Met police.
Figures released for the first time revealed 12,605 incidents where officers used force against people were registered in the three months to the end of June.
The data showed 45% of the individuals subject to force were white, 36% black and 10% from the Asian community.
Mr Charles was followed by officers in Dalston on 22 July and became ill when restrained by police after putting an object in his mouth.
Ms Abbott said: "The IPCC's update, coupled with the release of a Metropolitan Police report highlighting a disproportionate use of force against [black and minority ethnic] people, will no doubt cause deep concern and upset.
"Urgent work must be done to rebuild trust and links between the police and the community."
"There must be justice for Rashan and his family, but there is absolutely no cause for any more violence," she said.
The shadow home secretary has warned that findings of a probe into Rashan Charles' death will "cause deep concern".