Raymond Domenech refused to explain why he did not accept the offer to shake hands with Carlos Alberto Parreira at the end of France's defeat by South Africa.
France coach Domenech's reign ended with another lacklustre performance as a 2-1 defeat condemned the 1998 winners to an early exit from the World Cup after finishing bottom of Group A.
Domenech, who had led Les Bleus to the final four years ago, has endured a tournament to forget after Nicolas Anelka was sent home following the defeat by Mexico and the players refused to train on Sunday.
Further controversy hit the embattled 58-year-old at the final whistle of Tuesday's game in Bloemfontein when Domenech refused to shake hands with his South African counterpart.
No intention of replying
When asked why he snubbed Parreira's approach, Domenech said: "I have no intention of replying to this question.
"Is there another question?," he responded when pushed for an answer on the issue by another journalist and he offered the same comment when asked for a third time.
South Africa coach Parreira believes the snub was in response to comments he had made about France's controversial qualification for the finals when Thierry Henry's infamous handball helped to see off the Republic of Ireland.
Parreira said: "I believe it was because I had criticised his team after they qualified, but I really don't remember.
"This is what his assistants told me."