Henry appeared to handle the ball twice before feeding defender William Gallas, who bundled home from close range on 103 minutes to give France a 1-1 draw in the return leg of their playoff and a 2-1 aggregate win.
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The forward first stopped the ball from going out with his arm, then controlled it with his hand in a crowded penalty area and crossed for Gallas to give France the edge in extra time after they had struggled for most the game.
"Yes, there is handball but I am not the referee," Henry told reporters.
"I'm in the box, there are two defenders in front of me. The ball bounced off my hand, the referee did not see it and I played on.
"It doesn't change anything to the fact that I'm happy we have qualified.
Ireland were devastated after missing out on the World Cup because of what coach Giovanni Trapattoni called a "great mistake" by Swedish referee Martin Hansson.
"I told the referee that it is possible to make great mistakes," Trapattoni told a new conference after the game at Stade de France. "It is a bitter evening."
Trapattoni said he felt the referee should have talked to his assistants and to Henry before awarding the goal.
"I am sad because the referee had time to ask the linesman and I am sure he should have asked Henry as well," the Italian said.
"All the European people saw the game and what happened. France played a good game in Dublin but this time we played better and over the two games we deserved to go to South Africa," Trapattoni added.
"NOT VALID"
France defender Sebastien Squillaci said he realised the decisive goal was not valid but said such incidents just had to be accepted.
"It's part of the game, it played in our favour tonight, maybe some other time it will play against us.
"Of course Ireland will not he happy but we are happy the referee awarded the goal. We're competitors and we're there to win. The goal may not be valid but we'll take it."
France, who won the first leg 1-0 at Croke Park on Saturday, indeed looked nervous and clumsy until the closing stages while Ireland kept pushing and had the better chances but were denied by a string of great saves by France keeper Hugo Lloris.
France coach Raymond Domenech, whose job was on the line, said he had not seen the controversial goal properly.
"I didn't see the replay," he said. "From where I was, I couldn't see anything. All I know is the referee awarded the goal."
Domenech, under heavy criticism since France's Euro 2008 flop, praised Ireland for a spirited display.
