England's women have now lost three straight semi-finals following defeat to Japan in the 2015 World Cup in Canada and the loss to the Netherlands in Euro 2017.
After a relentless game in which England skipper Steph Houghton missed a late penalty, Neville chose an upbeat assessment, despite having said earlier that defeat would mean the tournament was a "failure".
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"That tells me that we’re closer than we’ve ever been. We came here to win and we didn’t do that," he said.
"Good luck to the USA. They showed they know what it takes to win football matches. Their game management was spectacular.
It was the most enthralling 90 minutes I’ve been involved in as a manager. We're knocking on the door now.
"The aim is for us to become the best, like America. We’ve still got a bit to go, but I won’t stop until we get there," said the former Manchester United defender, who took over the women's side in January, 2018.
Instead of a first World Cup final, Neville and the Lionesses head to Nice for the third place decider against the losers of Wednesday's other semi between the Dutch and Sweden.
That may be the game no-one wants to play but Neville said England could head there knowing they had given their all.
“I didn’t want to see tears. I thought the way we lost was exactly the way we wanted to play. The courage they had to play football and keep going, to battle; they left everything out there," he said.
"No regrets. We gave it our absolute all. We’ve had the best four to six days of our lives, so we didn’t want it to end. It’s not over because we have Saturday’s match. I don’t wallow and I won’t feel sorry for myself."
Neville said he felt the 84th minute penalty, awarded after video review, could have turned the game England's way.
Houghton's chance to level the game was saved by U.S. keeper Alyssa Naeher.
"When we got the penalty I turned to my bench and said we were going to win it, but it wasn't to be," he said.
"We knew it was going to be an open game and I felt they were starting to run out of steam in the second half.
"That is football and Steph Houghton has probably had the best season of her career.
"She had the courage to take the penalty and then keep playing football after. She is an amazing person and a world class footballer."
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