"I'm heartbroken but I'm very proud of the team because we fought so hard in this tournament. It was so close against the best team in the world but we are so disappointed," said Houghton who had a chance to level the game in the 84th minute but saw her weak penalty saved by U.S. keeper Alyssa Naeher.
"I got told today that I was on the penalties and I was confident because I had been scoring all week but I didn't connect with it properly and the goalkeeper guessed the right way," she said.
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Christen Press had put the U.S. ahead before Ellen White equalised for England in the 19th minute only for Alex Morgan to restore the lead for the defending champions.
"I thought we were the better side in terms of how we played football but, ultimately, lapses in concentration cost us," admitted Houghton.
White, who has scored six goals in the tournament, had a potential equaliser ruled out for offside after video review and was distraught at the end of the game.
"I'm going to cry. I'm devastated not to get to the final. All I feel is pride for my team mates. USA had an amazing match and we just couldn't match them. I'm proud to be English and I wish them all the best in the final," she said.
"We gave everything. In the first half we were sloppy. We got ourselves back into the game with the goal and it's bitterly disappointing. We've got an unbelievable squad and we had so much belief that we'd get to that final but we just couldn't do that on the day."
White was quick to offer support to her captain after the dramatic game.
"The person stepping up takes a lot of courage and we'll never put anything on Steph -- she's our leader. We'll rally around her and get ready for Saturday."
England will play the losers of Wednesday's other semi-final, between the Netherlands and Sweden, in the third-place game in Nice on Saturday.
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