England captain Harry Kane was gutted following the 2-1 loss and insists he will use their disappointing World Cup exit to be mentally stronger in the future.
"Absolutely gutted. We’ve given it everything and it’s come down to a small detail which I take responsibility for," he wrote on Twitter.
"There’s no hiding from it, it hurts and it’ll take some time to get over it but that’s part of sport.
"Now it’s about using the experience to be mentally and physically stronger for the next challenge. Thanks for all the support throughout the tournament – it means a lot."
Defender Harry Maguire had entered the World Cup under scrutiny having struggled to hold down a regular spot with his club side Manchester United, but his place under Gareth Southgate was never in doubt and the centre-back thanked the manager after their exit.
"Last night hurt. Absolutely gutted. Special thanks to Gareth and you amazing fans who kept belief in me," he tweeted.
"I love my country and I hope we made you proud."
Meanwhile, Declan Rice said disappointment was "all part of the journey" to success in the future.
The prime minister later took to Twitter, writing: "Harry and the team gave it everything but it wasn’t to be. They can hold their heads high tonight."
\u201cHarry and the team gave it everything but it wasn\u2019t to be. They can hold their heads high tonight. \n\nBest of luck to France in the next round.\u201d