The pair clashed twice, before Ibrahimovic scored the 78th-minute winner and celebrated in Onuoha's face.
Onuoha, 32, says he rejected the Swede's apology in the dressing room.
"Over here it is just a show for him. A lot of humans are scared of him - however he is simply a mere mortal," he said.
"First, he used to be very arrogant. Secondly, I thought: 'What is this man taking part in at?'
"This is no longer the way you are supposed to do it, mainly any one who is intended to be the face of the game right here and the game globally.
"I wasn't a fan before - and I'm virtually no longer a fan now."
What passed off and what used to be said?
The first flashpoint got here in the sixtieth minute, when 37-year-old Ibrahimovic was once booked for dragging Onuoha to the floor by his neck in an off-the-ball incident.
Onuoha stated the former Manchester United striker then made the threats to him following another venture shortly afterwards.
"This time he hit me on top of head. I was once more thinking: 'What is going on here?'" Onuoha instructed BBC Sport.
"He saved saying: 'You know what? I am going to damage you. I am going to do you. You just watch, there is enough time, I am going to do you.'"
After Ibrahimovic scored, Onuoha claims the former Sweden worldwide told him: "You don't mess with me in the game. You don't mess with me."
Once the recreation was over, Ibrahimovic came into Real's dressing room, later telling reporters: "I went to shake their hands, no big issues."
Describing the moment, Onuoha, who joined Real in 2018, said: "He commenced coming closer to me and said, 'have you calmed down, massive man?'
"The quantity of disrespect he confirmed me on the discipline - I desire to let things go, but I can't let them go, especially when it is so raw.
"The way he got here in was once almost conceited in itself, attempting to be all friendly. But this is the guy who fouled me on the field, tried to embarrass me when they scored, then he comes in to try and allegedly apologise.
"I do not think he is a accurate person, so I am no longer going to offer my hand and, in no unsure terms, I informed him to get out."
'This man is disrespectful'
Asked about the confrontation, Ibrahimovic informed reporters: "What happens on the area stays on the field.
"I like to experience alive. I like when it becomes duels and that, due to the fact every so often - no longer that I fall asleep - however I don't sense alive if they don't truely prompt me. When I get angry, I feel good."
Onuoha replied to these remarks via saying: "If that is how he needs to encourage himself, then whatever. He was having a terrible game earlier than that. He need to have thought I was straight out of college over here, the way he was speaking to me."
Asked if he would receive a proper apology, Onuoha added: "No, I assume it is fake. He nonetheless thinks he is higher than me as a human being and I don't have time for people like that.
"Even when I played against [Juventus forward] Cristiano Ronaldo when he used to be younger, he'd be a bit temperamental, but that used to be his pure wish to win, no longer always to disrespect the opponent, which is what I assume this man is doing.
"It seemed like it was me upsetting him more, which is loopy from a man who will go down as one of the best of all time in Europe."
Asked about the teams' next assembly in Utah in September, Onuoha replied: "The final time we played them at domestic we beat them 6-2. If it is some thing even close to that it will be a very accurate day with lots of celebrations to rub in his face."
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