"We want to be a team who are hitting quarter-finals, semifinals and finals. That's what we aimed to do in the long-term. We've proved to ourselves and our country that is possible.
"Now we have a new benchmark, a new level of expectation, a new scenario. But many of these players have come of age on an international stage. I couldn't be prouder with what they've done. For everybody in our party, I wanted them to create memories that are with them forever, for them and for others.
"I think we've all had an incredible experience. For me, that's what sport should be about.
"You give everything you have, build friendships with your team, give everything for your country and play in a way that you hope connects with the fans. The players have played and conducted themselves in a manner that has absolutely done that.
"If we've brought joy back home, which I know we have, then that's been worthwhile. We should be proud of that. We're hugely disappointed not to take the country one step further and give them everything they hoped for. But, in time, I'm sure we'll reflect on the progress made."
Kane, who remains on course to win the Golden Boot, said: "It hurts, it'll hurt for a while, but we can hold our heads up high. It was a fantastic journey, we got further than anyone thought we could, we've just got to learn from it.
"It's tough. We're gutted, you know. We worked so hard. The fans were amazing. It was a tough game, a 50-50 game. I'm sure there was stuff we could have done better, but we worked as hard as we could.
"We created some good chances, being 1-0 up. Maybe we dropped too deep at times. In big games, it's small margins. There's a lot we could have done better, but they played well. It's been great to get to this stage, but we wanted to go on and win it.
"We've fallen a bit short. It just hurts. It shows we can win knockout games — the next stage is to go one further. We've got to dust ourselves down and go again in a couple of years.
"There are a lot of positives to take from this tournament. It's a big stepping stone from two years ago."
England must stay in Russia to play for third and fourth place against Belgium in St Petersburg on Sunday (NZT) and Southgate added: "The honest thing is it's not a game any team wants to play in. We have two days to prepare. We will want to give a performance of huge pride, no question about that.
"It will be a really difficult task to assess everybody over the next 24 hours and get them mentally back to where we want them to be for a game like that, but that will be the challenge."
- Telegraph Group Ltd
