Referring to the assassination off Co Sligo in the Irish Republic, he said he told the royals that he recognised they had lost a relative.
"I said to the Queen and the Duke they too had lost a loved one," he said.
Mr McGuinness revealed some of the detail of the private meeting during a talk show on RTE television.
The killing was discussed briefly after an historic handshake between the pair which has been hailed as a watershed moment in Anglo-Irish relations.
Mr McGuinness has not discussed any of the detail of the meeting until now. When he left the theatre he would only say that the Queen was very nice and that he was still a Republican.
More top news
Prince Harry has visited a children's home founded by the controversial religious sect known as the Moonies during his tour of the Caribbean
Cloud continues rolling in from the west overnight which, combined with fresher winds will keep temperatures above freezing here.
Charlton Athletic Football Club have launched an internal investigation over an allegation of historical sexual abuse.