"I rarely let my emotions get the best of me," fullback Lawrence Vickers said. "Today they did, but this was the place to do it."
Owner Jerry Jones spoke with Brown's mother twice on Sunday. The team plans a memorial on Tuesday.
Jones wishes more had been done to help Brent, who had a DUI arrest in 2009.
"Personally, I have spent a lot of time over the past 12 hours thinking what might have been said and done," Jones said. "I know there are many things that might have been said or done. So the answer is yes. But I know that's the way things happen when you have a tragedy."
Cornerback Brandon Carr was with the Chiefs last season and was close to Belcher. He attended a funeral on Saturday, then rejoined the Cowboys as they started dealing with their own grief.
"Honestly, I couldn't do it myself," said Carr, who had an interception against Cincinnati. "My teammates have had my back since Day 1 with what transpired last week (in Kansas City) and then today."
Players around the league also were touched by it.
San Francisco 49ers defensive lineman and special teams standout Demarcus Dobbs thought about it before a home game Sunday against Miami. Dobbs was arrested early Nov. 30 — his 25th birthday — on suspicion of driving under the influence and possession of marijuana. He missed last week's game at St. Louis but was active for Sunday's game with the Dolphins.
Authorities said Dobbs was alone and involved in a single-car accident in which he hit a chain-link fence and a bush but didn't sustain any injuries.
"It was a wake-up call to me what happened to me," Dobbs said on the field before the game. "The thing that happened in Dallas, it makes me grateful that God was looking out for me. It could have been a lot worse in my situation.
"What happened in Dallas is unfortunate. It just goes to show what could have been. I'm grateful that I'm here and able to be on the team and go on and continue my life. That saddened me to hear that, but it made me count my blessings even more."
AP Sports Writer Janie McCauley in San Francisco contributed to this report.
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