He has apologised and said he will donate the fee he received for appearing as an expert on the BBC.
Given, a former Republic of Ireland goalkeeper, spoke on the Final Score programme on Saturday, describing Nancy's 33 days at Celtic as "terrible from start to finish."
He described it as an "absolute holocaust".
The statement sparked strong reactions and Given has since apologised on social media, saying he did not realise what the word meant.
"We all have areas where our knowledge is lacking and I hope to use this as an opportunity to become better informed," Given writes.
He says he is sincerely saddened and apologises unreservedly to anyone who has been offended.
"I will donate my fee from today's broadcast to the Holocaust Educational Trust," Given states.
The Holocaust, in Swedish Förintelsen, was the systematic genocide of around six million Jews by Nazi Germany during World War II. Roma, homosexuals, people with disabilities and political opponents were also systematically murdered by the Nazis.
Shay Given, 49, played for clubs including Newcastle, Aston Villa and Manchester City and earned 134 caps for Ireland.
