Wendie Renard headed a late reply to ensure a tense finale, but the US survived a raft of late pressure to move a step closer to defending their title.
"That was the most intense match I have ever been a part of," Ellis said.
"A win's a win in a World Cup. I haven't seen many pretty games in a World Cup.
"We trained for a back-five for moments like this. France are an incredible team. The surge from the fans was intense, like a tsunami.
"To have flexibility and to know what card we needed to play at each particular moment. I credit the players. They've taken everything on."
Much of the build-up to the match had been dominated by a row between Rapinoe and US president Donald Trump but the 33-year-old midfielder did her talking on the pitch on Friday night.
She said: "We have such a tight group. It's a group that just wants to win. Our bench was huge. They're huge every night. They're in it. That helps a lot. They're screaming at you and encouraging you. Everyone understands the gravity of the night. It's phenomenal."
France head coach Corinne Diacre was proud of the way her team acquitted themselves in defeat after their hopes of lifting the world cup on home soil ended in heartbreak.
"I said they shouldn't have any regrets apart from a mistake on the opening goal that we conceded," said Diacre.
"They did win something tonight, they won the hearts and minds of a number of people. When you go out as host nation, you're not happy. So they're sad. We had a lot of hope, but that's the way things go.
"I'm not the kind of person to give up. I still have work to do. There are still certain things we need to fine tune and work on together.
"Yes, it is a failure on a footballing level. We're a long way off our target but I hope we have retained something elsewhere, and I hope we have won over the hearts and minds of the public and helped the women's game go further and move into that next level.
"We showed we're not too far off the USA side. I've never seen a USA side switch to a five-player back line, so it's a sign we're making progress."
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