Gallas headed in the winner after Thierry Henry appeared to twice handle the ball before crossing.
Ireland lost their play-off 2-1 on aggregate, following Gallas’ controversial winner.
Trapattoni said: “I am not only disappointed, I am also sad. It is a bitter evening.
“It’s a bitter situation. I would prefer to have gone out on penalties.
“I am sad because the referee had time to ask the linesman. I am sure he should have, and he could have confirmed it was handball.
“I am upset. We speak many times about fair play. I go to schools and speak about fair play. I speak with the young kids about sport. It’s important in life.
“Everybody saw the game. You know what happened.”
Trapattoni added: “France played well in Dublin, but tonight we played better.
“And over two games, we deserved to go to South Africa. But the result is different. We can only wish them well. They can do well in South Africa.”