The US had been the last of the three co-hosts of the World Cup left in the competition following Mexico’s defeat by England on Monday and Canada’s loss to Morocco on Saturday.
Mauricio Pochettino’s side were hoping to reach the quarter-finals for the first time since 2002 but underwhelmed in their biggest men’s match in a generation.
But the build-up to the fixture was overshadowed by Fifa’s decision to put Balogun’s one-match ban on hold.
The 25-year-old had appeared certain to miss the match in Seattle after being shown a straight red card for a foul on Bosnia-Herzegovina defender Tarik Muharemovic in the previous round.
But on Sunday Fifa suspended the automatic one-match ban for 12 months, leading to widespread criticism.
Trump said on Monday, before the tie, that he asked Fifa to review Balogun’s ban, which he said would have left a “big stain” on the tournament.
Balogun was unable to add to his three goals though, with his only big chance, from a tight angle, smartly saved by Belgium keeper Thibaut Courtois in the final 10 minutes.
The pressure appeared to get to US who struggled to create meaningful chances.
They have now fallen at the last-16 stage at four of the past past five World Cups.