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
Most children are happy to let their teeth come out naturally but for one Florida boy, a little extra horsepower was called on.
Travellers hoping to get away for the Easter weekend are being warned of potentially serious problems on the road and rail networks.
Left-footed footballs, backwards web searches, police camels and an eco-friendly Jeremy Clarkson are among today's traditional tall tales.