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Kane took responsibility for England's World Cup exit after blazing a late penalty over the bar in the 2-1 defeat to France, saying he will "have to live with" the error.
England more than matched France during the tense quarter-final at Al Bayt Stadium, with Kane's 54th-minute penalty cancelling out Aurelien Tchouameni's first-half opener from the spot after the France midfielder fouled Bukayo Saka in the area.
However, Olivier Giroud restored the holders' lead in the 78th with Kane was unable to score again when Theo Hernandez conceded an unnecessary spot-kick, firing over the crossbar.
The miss left Kane level with Rooney as England's all-time top goalscorer with 54th international goals, while the Three Lions suffered a seventh World Cup quarter-final elimination – a tournament record.
The skipper speaks to @itvfootball following tonight's defeat to France...pic.twitter.com/wYNUtzoUoY
— England (@England) December 10, 2022
Speaking to BBC Sport after the defeat, England's captain fronted up to his mistake and praised his teammates for going toe-to-toe with the world champion.
"It's tough to take for me personally and for the team," he said.
"I couldn't be prouder of the boys. We had better spells, better chances but football comes down to small details.
"As the captain and the one who missed the penalty I take responsibility for that.
❌ 84' @England🏴 hopes of a second leveller are blown over the crossbar as @HKane skies his effort from 12 yards after a VAR decision awarded another penalty. What drama! #ENG 1-2 #FRA | Follow it LIVE HERE 👉 https://t.co/WFC9mPURKN#FIFAWorldCup #ENGFRA #Qatar2022 pic.twitter.com/7LApwp55jg
— beIN SPORTS (@beINSPORTS_AUS) December 10, 2022
"I can't fault my preparation or the details before the game.
"I felt confident taking it, I just didn't execute it the way I wanted to.
"It will be something I have to live with and take on the chin.
"The team is in a really good place and there will be highs in the future. Standing here now, we are gutted it has come to an end as we had full belief we could go all the way. We can be proud of what we've done."
Henderson expects Kane to bounce back from penalty miss
Kane is the first player to both score and miss a penalty in a World Cup match (excluding shootouts) since Michal Bilek did so for Czechoslovakia against the United States in 1990.
He has scored more World Cup penalties than any other player (four).
The miss leaves Kane level with Rooney on 53 England goals and the Manchester United great expressed his support for the Three Lions skipper after the loss.
Level on 53 goals for the #ThreeLions!@HKane 🤝 @WayneRooney pic.twitter.com/GErwW5kmMz
— England (@England) December 10, 2022
"Absolutely gutted for the lads but proud of the way they've played this tournament and they should be proud," Rooney said on Twitter.
"Congratulations to Harry Kane on equalling the record, he'll be on his own soon and I couldn't think of anyone better to take over. Keep your head up Harry."