Charles De Ketelaere gave the Red Devils an early lead, tapping in after Leandro Trossard's clever work down the left carved the USA defence open. The response from Mauricio Pochettino's side was swift and somewhat fortunate, as Malik Tillman's free-kick took a wicked deflection past Thibaut Courtois to make it 1-1.
Belgium needed barely 60 seconds to restore their advantage, De Ketelaere striking again to complete his brace and put the Europeans back in front. The USA's night unravelled further when goalkeeper Matt Freese's error gifted Belgium a third, and substitute Romelu Lukaku added gloss to the scoreline with an injury-time strike to seal a 3-1 victory.
Garcia was full of praise for the travelling support and his players after the win.
"To everyone who got up in the middle of the night to support us, I'd like to say a huge thank you," he said, quoted by FIFA. "They should be happy and proud of their players today. We showed that Belgium is a great football nation."
USA coach Mauricio Pochettino cut a dejected figure afterwards, admitting his side never got going.
"It was really tough from the beginning. We congratulate Belgium, they were better than us. It wasn't our day," he said. "We need to learn, we need to assess the game and understand why we did not approach the game in the same way we did as we did in the rest of the World Cup."
Playmaker Christian Pulisic echoed his manager's frustration despite pride in the run.
"Up until today, we are very proud and I thought we did a lot of good things, but for sure it was just a disappointing way to end," he told FIFA. "We played against a very good team that was very clinical in both ends of the pitch, and we weren't exactly so... that's where the game is won in the boxes, so it was not quite enough from us today."
Full-back Sergino Dest was similarly downbeat.
"I don't have a lot of words, we're really disappointed. It just wasn't our day," he said. "We are proud but we felt that we could have done more than what we did, so at the moment we're just disappointed."
Defender Chris Richards, though, pointed to the bigger picture for a young USA squad: "Hopefully this is just the beginning of what's to come for this group and this federation.
"I think it should be the normal, at least the quarter-finals. Hopefully we've drawn a line in the sand for the future."
Pulisic added: "We did the best that we can. I hope that people can see that and believed in us and there's more than what we wanted to accomplish."
Half-time substitute Gio Reyna also reflected on the exit.
"It was one of those days where things did not fall our way. It wasn't our best game, I felt we could have managed a couple of moments a bit better. They were the better team today," he said. "We all really enjoyed our time together. It's been one of my favourite experiences as a player so far in my career."