Uruguay captain Jose Maria Jimenez said players were trying to protect their families from violent fans.
Uruguayan footballers clashed with Colombian fans after their Copa America semi-final defeat, with security personnel having to intervene to restore order.
After Colombia's 1-0 win in Charlotte, North Carolina, on Wednesday, a video posted on social media showed what appeared to be a Uruguayan player climbing into the stands and exchanging blows with opposing fans.
The South American Football Confederation (CONMEBO) said it was investigating the incident and strongly condemned any act of violence affecting football.
“Our work is based on the belief that football connects and unites us through its positive values,” regional football governing body CONMEBOL said.
“Intolerance and violence will not be tolerated, on or off the field.”
Uruguay players Darwin Nunez and Ronald Araujo were among those at the forefront of the melee, and captain Jose Maria Jimenez said the players were trying to protect their families.
“Let me say something before I get interrupted because they don't allow me to speak on the microphone. They don't want me to say anything about what's going on, but this is a disaster,” Jimenez said in the official broadcast.
“Please be careful. There are families in the stands, small babies. It was a disaster. There was no police, we had to protect our families.”
“This is the fault of two or three people who have had too much to drink and don't know how to handle it.”
Players and staff from both Colombia and Uruguay also clashed on the field after the final whistle.
“I thought the incident was just an altercation in midfield, so I saw it and went to the dressing room,” Uruguay coach Marcelo Bielsa told a news conference.
“I thought they were just thanking the fans for their support. But unfortunately, I learned there were some issues over there.”
Jefferson Lerma's first-half header secured Colombia a place in Sunday's final, with Uruguay set to face Canada in the third-place match.