Les Bleus squandered a 9-5 lead to go down 14-9, Jonny Wilkinson finishing the hosts off with a drop-goal and a penalty in the final six minutes.
The French recovered from losing their opening match of the tournament to Argentina by winning four straight games, including a sensational 20-18 victory over New Zealand in the quarter-finals last weekend.
Beating the world champions was challenge too far but Laporte - for whom this was his last match - was full of praise for his men.
"I would like to congratulate my France team," said Laporte, who will now take up a role in the French government.
"We put our heart and soul into this competition and this game. We are a great rugby nation, and the players can hold their heads up high.
"When you see the path that we followed, you can say we did well.
"We are very disappointed as the aim was to win this match and get into the final. It stops tonight but I don't think it was a bad World Cup by us."
Laporte felt the teams were evenly matched at the Stade de France, adding: "The England team were strong but we expected this kind of match.
"They occupied a lot of territory but we were not able to do that. We were not able to make the break and not able to score.
"It was difficult to get back into match when we went behind at the end. We weren't in their 22 enough but it was two teams who were pretty equal throughout. It was that kind of match."
Fabien Pelous, France's veteran lock, was forced off midway through the first half with a rib injury, to be replaced by Sebastien Chabal.
The Sale Sharks talisman has been used as an impact player this tournament but had to play an hour here.
Laporte said: "Pelous going off was one of the important moments. Sebastien played well but his power lost a bit because he had to play for an hour.
"We would have preferred to use Sebastien late on, after using Pelous more. It didn't prejudice us but it did not help us."
Les Bleus captain Raphael Ibanez was distraught after seeing his team's World Cup hopes die at the hands of England at the semi-final stage for the second time in four years.
"It is difficult to find the words to express my disappointment," he said.
"We thought this would be the match, but it was difficult in the end and the result did not go in our favour.
"We will need a few days to digest this. But this is sport - it goes one way or the other.
"England deserved to win and they took their chances when it mattered."
Wilkinson missed his first three kicks at goal but produced the goods when it really mattered in the final few minutes
"You have to recognise the cool of Wilkinson," said the Wasps hooker.
"In these important moments, he is a great player, that's all you can say.
"But tonight, I don't want to talk about England. We wish them good luck but personally I would like to talk about our courage in this competition.
"The Argentina defeat was difficult to take, but we have to hold our heads up that we could come back.
"I want to emphasise the team spirit and thank the coach for his efforts."