"We want to be sure as best as possible that something like this does not happen again."
Ms Abbott blamed the "hostile environment policy" for the scandal.
She said: "The deaths of these British citizens in Jamaica shame this government and the Prime Minister, who is the architect of the hostile environment policy that saw these British citizens sent to Jamaica.
Diane Abbott said the deaths 'shame the government' (PA)
"Our fellow citizens dying thousands of miles from their homes, families and friends and our health service is the latest tragic injustice suffered by our fellow citizens as a direct result of the Tories' hostile environment.
"The Prime Minister must personally apologise to their families and loved ones."
The Home Office said in a statement on Friday: “The experiences faced by some members of the Windrush Generation are inexcusable. The home secretary and the immigration minister have said it is their priority to right the wrongs that have occurred.
“Our historical reviews into removals and detentions have identified 18 people who it is believed could have been wrongfully removed or detained. Three of the 18 people have been confirmed as having died. The home secretary will be writing to the families of the deceased as well as the other 15 people identified to offer a personal apology. We are working closely with Caribbean high commissioners and governments to do this.”