He added: “We all have areas of ignorance in our knowledge, and I hope to use this as an opportunity to become better educated going forward.
“I am genuinely mortified and apologise unreservedly to everyone offended, and will be donating my fee from today’s show to the Holocaust Educational Trust.”
Final Score presenter Jason Mohammad apologised later in the show for the “inappropriate language” used.
Frenchman Nancy was sacked last week following Celtic’s 3-1 defeat by Rangers – his sixth loss as manager in just eight games.
His 33-day stint as Celtic boss was the shortest reign in the club’s history.
The Holocaust, carried out by Nazi Germany during World War Two, claimed the lives of an estimated six million Jews.