United States coach Mauricio Pochettino praised his players' unity after they saw off Bosnia 2-0 with 10 men on Wednesday but railed against Balogun's dismissal for "accidental" contact in the round-of-32 clash.
The win was the U.S.'s first in a World Cup knockout since 2002 and set up a last-16 showdown with Belgium.
"It's difficult to describe our feeling, because I think they were amazing, and (there is) no easy game in the World Cup," he said.
"I think the maturity of the team is amazing in the way that we are growing in the last five-six weeks."
Balogun, who scored his third goal of the tournament near halftime, will miss the biggest match of his career, though, after getting a red card for planting his foot on Tarik Muharemovic's ankle.
Bosnia coach Sergej Barbarez said the decision, confirmed after a VAR review, was fair but Pochettino saw it differently.
"Never was this a red card. Watching it on TV, never was there intention to step (on) the player," he told the post-match press conference.
"That was a normal action in football. That happened by accident and it's never intentional. That is why for me it was never a red card."
Pochettino said Balogun was disappointed and sad in the dressing room.
"But he's also happy because we qualified... He needs to understand that this type of situation happens," he said.
"I hope that, for sure, he is going to be able to help us again. I hope that we go to the next round."
Pochettino became the first U.S. men's coach to win three World Cup matches, and belted out "Country Roads" with fans in the terraces as he hugged players and staff after the final whistle.
With Christian Pulisic starting, Pochettino reverted to the same 11 he deployed in the opening 4-1 thrashing of Paraguay but they were kept at bay by the stacked Bosnian defence until the cusp of halftime.
It took a touch of fortune to break the deadlock, with Balogun swooping on a deflection to fire a low shot home.
Malik Tillman then doubled the lead with a free kick after Balogun's red card to seal the win.
"It was amazing, Malik is an amazing player, full of talent," said Pochettino.
"We knew that he has that talent to do the free kick ... to do what he did. So happy for him."