Kane admitted that the defeat was "painful", but believes that the team can be proud of their run and is confident that there are plenty of bright signs for the future.
"A lot of emotions today. First of all I'm so proud of this team and staff for giving everything we could over a long period of time together. We have overcome so many challenges that have haunted England in the past," Kane wrote in a social media post.
"We have reconnected with our amazing supporters and have enjoyed this incredible experience together. It wasn't the outcome we wanted and as painful as it is right now, I'm sure we will learn an awful lot from last night's game.
"It's time now to hold our heads high as a nation and be proud of each other. I'm excited to be part of this team and the challenge to improve going forward. Thank you all for your support!"
Kane still leads the race for the Golden Boot and could still add to his tally of six goals in the third-place playoff against Belgium on Saturday.