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.