Luis Suarez opened the scoring for the hosts from the spot before Alexis Sanchez equalised for Chile early in the second-half.
The visitors looked more likely of scoring in the closing stages and were denied a penalty in the dying stages after the ball had struck the hand of Uruguayan defender Sebastian Coates in the box.
VAR seemed to review the incident but no spot-kick was awarded with Coates deemed to have put his hand to his side rather than towards the ball.
The decision would be costly as Uruguay went up the other end and scored an injury-time winner via substitute Maxi Gomez.
Bravo, who was unable to play for Chile due to injury, wasn't happy his team weren't awarded a penalty at such an important moment and took to social media to express his anger.
"I don't believe you...impossible when these things happen. Terrible!!" he tweeted.
"If you call what we all see, we'd get 1-2 ahead if you awarded the penalty in minute 90. And you killed the game. With details like these it's impossible to score. Unfortunate!!!"
— Claudio Bravo Muñoz (@C1audioBravo) October 9, 2020
Prior to the match, Bravo had wished his team-mates luck as they look to qualify for the 2022 World Cup in Qatar.
"The road is very long, but the satisfaction in the end is unimaginable," he posted on Twitter.
"For those who are just getting started, don't miss opportunities and for those with more experience, just keep believing @LaRoja forever!!! Let's go...one goal only."
Chile failed to qualify for the 2018 World Cup in Russia but had made it to the previous two tournaments where they reached the Round of 16 both times.
Reinaldo Rueda's side will look to bounce back from their controversial defeat against Uruguay when they host Colombia on Tuesday. Uruguay, meanwhile, will travel to Ecuador on the same night as they look to extend their undefeated streak to eight matches.
Bravo, who is currently playing club football for Real Betis, will no doubt be watching both games closely.