Balogun was sent off in the 64th minute of the USA's last-32 win over Bosnia and Herzegovina on Wednesday, having already put his side ahead.
The striker was judged by the referee, following a VAR review, to have stamped on the back of defender Tarik Muharemovic's foot. Replays showed Balogun's outstretched foot landing on his opponent's turning ankle as the pair competed for the ball.
Balogun also appeared to pick up an injury in the collision, but the referee opted to send him off after consulting the pitchside monitor. Pochettino was adamant afterwards that the challenge carried no malicious intent.
"For me, never is a red card," said Pochettino. "It never was (his) intention to step on the player.
"It was a normal action in football, that you are fighting for the ball, and your feet land, no? Yeah, maybe it was a little bit tough, the scene, to watch. But I think it never was intentional."
Christian Pulisic backed his manager's assessment of the incident, insisting his teammate had done nothing to warrant such a severe sanction.
The USA forward said Balogun "didn't deserve the red card," describing the decision as "unfortunate."
Under FIFA regulations, the sending-off triggers an automatic suspension for the USA's next match, one that cannot be appealed, a FIFA spokesman confirmed to reporters.
Pochettino suggested he still hoped the ban could be overturned.
He said it "should be fair" to appeal the decision, but admitted he would have to weigh up "different options" if that route was unsuccessful.
Ricardo Pepi, who plays for PSV Eindhoven, filled in up front when Balogun was rested for the final group-stage match against Turkey.
Balogun was born in New York but raised in England before qualifying to represent the USA, and has become a key figure in Pochettino's forward line at this World Cup.
The 24-year-old has scored three times in the tournament, including a brace in the opening win over Paraguay, leaving him just two goals shy of Landon Donovan's all-time USA World Cup record of five.
Pochettino admitted the red card had left Balogun with mixed emotions heading into the Belgium tie.
"He's very disappointed, because I think it was an action that was unintentional. But also he's happy because we qualified," said Pochettino. "We cannot do nothing to change that feeling. That is over. That is football. He needs to understand that this type of situation happens."
Pochettino ended on a note of optimism over his side's prospects without their in-form forward.
"For sure he is going to help us to perform. I hope that we can go to the next round and (he will) be available again."