Afterwards, the former Munster MEP said he had no regrets about his decision not to stand again after spending 15 years in the parliament.
He is now officially unemployed and said he will not make any decisions about his future until after a long holiday with his wife and family.
The only thing about his future he was sure of was that he will not return to Irish politics. “Absolutely not,” was his reply.
Many believed Taoiseach Bertie Ahern would help promote him as president of the European Commission, but this did not happen.
Mr Cox refused to comment on this but said he was not pessimistic or negative about his future. “I have no idea what I will do but whatever I do I am sure I will make a success of it,” he said.
After the election of the Spanish Socialist member Josef Borrell on the first count with 388 votes to 205 for his nearest rival, the new and the former president had a private lunch.
“He is not a newcomer to politics but he is a newcomer to this house so he wanted to talk to me about the job,” said Mr Cox.
Mr Borrell, a former aeronautics engineer with a masters and PhDs in economics and applied maths from Madrid, Paris and Stanford University in California, was a minister in the Spanish government of Felipe Gonzalez for many years.
The son of a baker he left school at 10 and completed his secondary education at home while working in the family business.
From a small village in the Catalan Pyrenees, where his first language was Catalan, he was unable to address the parliament in his native language because it is not an official EU language.