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
An Irish nanny freed after baby murder charges in the US were dropped describes her 'nightmare' and branded the prosecution a 'scandal'.
A man became so frustrated with noise from a nearby building site that he shot a builder with an air rifle, police say.
A backbench revolt over proposals to ease purdah restrictions on the EU referendum has led to a government climb down.