The 27-year-old died following a "catastrophic" series of errors in the operation which ended in his death, said the latest report.
Talking to the Brazilian press from London, a Menezes's cousin, Alex Pereira told about the family's plan after this latest verdict: "Now, as in princess Diana's case, we are going to file a more detailed suit showing who really made a mistake.
"In these just-announced proceedings, the main witnesses were not heard, as well as the civilians who were in the subway and the policemen who shot Jean."
The new lawsuit should be filed on April 2008. "There was no justice done," Pereira added. "They punished the car, but they left the driver go free."
For him, the fine given Scotland Yard is no punishment. "The money goes to the State but who's giving the money is the same State. And the money comes from our pockets."
Pereira said that Jean's mother, who lives in the city of Gonzaga, in the state of Minas Gerais was happy to hear about the guilty verdict. He also classified as "ridiculous" Scotland Yard lawyers' charges that Menezes had cocaine in his blood.
The young Brazilian electrician was shot seven times by specialist firearms officers at Stockwell subway station after being mistaken for failed suicide bomber Hussain Osman.
Prosecutors at the Old Bailey set out 19 alleged failings in the police operation in the hours leading up to the shooting on July 22, 2005.
The jury convicted the force on the second day of its deliberations. The Metropolitan Police was fined US$ 361,000 and ordered to pay US$ 794,000 costs by trial judge Mr Justice Henriques.
In a rider to the verdict, the jury cleared the operation commander Cressida Dick, with the foreman saying: "In reaching this verdict the jury attaches no personal culpability to Commander Dick."
Metropolitan Police Commissioner Sir Ian Blair was in court to hear the verdict. Blair, whose office was on trial during the case, said before it started that he feared a guilty verdict would have a "profound" impact on policing throughout the UK.
The trial and investigation is estimated to have cost around US$ 7.2 million in public money.
Bzz/Mercopress