Cox was left in a coma and with life-changing injuries following the incident outside Anfield prior to the first leg last April and a fund was launched to help cover the costs of the 53-year-old father of three's rehabilitation.
Liverpool boss Jurgen Klopp and Everton defender Seamus Coleman are among those to have contributed already.
On Thursday, Roma released a statement confirming the club will donate €100,000 through its Roma Cares foundation, with Pallotta to make a personal donation of €50,000, while the club promised to work with Cox's family to support additional fundraising efforts.
November 15, 2018
Cox's wife, Martina, added: "Our life has been turned upside down by what has happened to Sean.
"There is no sign of Sean being able to return home any time soon and even with extensive specialist rehabilitation efforts, which will take years, he will require care for the rest of his life.
"We are hugely appreciative of today's donation by AS Roma and Mr Pallotta, and more particularly by committing to meaningful assistance over the coming years with the struggle Sean is facing into."