The Three Lions suffered an extra-time 2-1 defeat at the hands of Croatia in Moscow, after a roller-coaster game which saw England take an early lead through Kieran Trippier, only for a second-half equaliser from Ivan Perisic to take the game to extra time and set up Mario Mandzukic's late victor.
Walker insisted England would be motivated to beat Belgium on Saturday and finish third "because they got one over on us in the group stage", and went onto speak about using this World Cup as a platform for future success.
Kane had lead England to their first World Cup semi-final since the Italia '90 tournament 28 years ago, and in doing so scored a record amount of goals.
But it took just five minutes into the semi-final for Trippier to write his name on the score sheet.
The referees clearly didn't agree with the supposed loophole, leaving England players red faced in the middle of the pitch.
"It's not something I'm really thinking about at the moment to be honest, it's not the game we wanted to be in", Kane admitted.
The game went to extra time after neither side could find a victor in normal time, where Croatia continued their dominance.
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"The honest thing is it´s not a game any team wants to play", Southgate admitted. I think knockout football is about fine margins and when you have good spells against fine sides you need to take your chances.
Walker talked about a huge shift in the way that the national side are viewed after years of apathy and frustration - "We've brought fans back in love with the English team" - and he could not speak highly enough of the part that Southgate has played in helping to turn things around by instilling the players with the belief to go out and express themselves.
For Croatia, it's on the brink of arguably the most shocking World Cup title run in modern history.
MOSCOW, RUSSIA - JULY 11: Jamie Vardy, Dele Alli of England following the 2018 FIFA World Cup Russia Semi Final match between England and Croatia at Luzhniki Stadium on July 11, 2018 in Moscow, Russia. It went into extra-time and Gareth Southgate replaced Ashley Young with Danny Rose on the flank.
Kane revealed the plan is to "build on foundations" set in place by the 47-year-old manager, who is still a rookie on the global stage. "We are a nation of people who are proud, never give in and have character". "Nothing he is going to say is going to make us feel any better", Kane said.