The Champions League and Premier League winning defender bounced back from an earlier international snub to book his place at the final tournament – but that was snatched from him by injury.
Despite his heartbreak, Alexander-Arnold is likely to quickly turn his attention to the new season with Liverpool, in which they will go out to reclaim their title after a third-place finish.
Klopp will have been boosted by Southgate’s latest update, which suggests he will be fit to return alongside Virgil van Dijk come September.
Southgate said: “The one thing I was pleased about is that immediately after the game, I didn’t like the look of the injury.
“At least it sounds as though Trent should be fine for pre-season and for next season.
“So that is a small – very small – positive in the situation.
“Of course, he was very upset, bitterly disappointed. In those moments everybody is thinking about him.
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“It’s heartbreaking, really, for any player to get to the eve of a major tournament, be named in the squad, and then miss out through injury.
“You know how rare these opportunities are – even though he’s a young player who’s going to have those opportunities again.
“It’s a really difficult moment for him especially. It’s a big disappointment for us of course, as well.
“But you can’t help but first and foremost feel for Trent in this situation.”
Klopp said of his right-back following recent criticism: “I don’t think he has to prove anything, to be honest.
“You can play the best season of your life and the coach of the national team has to make decisions and we respect that.
“The only thing Trent is doing is playing his best football. In the last 10 days, twice he’s played outstanding and now he scores a goal. The most important thing is we stop talking about it.”