Mario Lemina is stepping down to be replaced by Nelson Semedo.
"We've decided to move the captaincy to Nelson and Nelson will captain the group from now on," said O'Neil.
"Of course, the other night sparked the conversation, but it was an important conversation that had to be had. Mario and myself have a good understanding now of how we move forward and what it looks like.
"We've spoken a lot this week - me, Mario and some of the other senior players. What happened after the game can't happen.
"We all understand emotions can rise, that we're in a tough moment and everyone's fighting and giving everything under big stress and pressure. But they're scenes we won't see again, definitely."
He added: "The discussions with Mario were good. We get on very well and he's been a big part of what we've been able to do here, especially since I've been here. We have a large amount of respect for each other.
"These things - sometimes they can be tough to deal with and sometimes you can come out of them in a good spot, and I feel like we have.
"He'll still be around that group of senior players who lead the team, but at this moment we feel it's best for Nelson to lead the group."
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