The Argentine took out both reigning champion Lando Norris and Alpine teammate Pierre Gasly on lap 35 in Baku, after a restart following a safety car intervention.
Colapinto apologised for his error, and a frustrated Norris initially called for him to be banned before also saying sorry for his reaction.
Briatore chose not to drop Colapinto, who has made peace with his team and will retain his drive at this weekend's Bahrain GP in Malaysia.
"There are times in the team when everyone is angry, and it's tricky to move forward," Colapinto told reporters at the Sepang International Circuit.
"But the important thing is that you always find a way.
"Flavio is a great team leader. He's really one of the best I've had in the sport, of course, since I started.
"He's very good at these situations, knowing how to manage them and knowing how to make the team better. So, I've always trusted him in this kind of stuff."
A furious Briatore had said he would reflect before deciding on what action to take over the crash, which cost Alpine a solid points haul.
Colapinto said he returned immediately from Baku to the team's base in southern England to resolve the problems.
"Of course, Flavio was angry, as everyone in the team was angry.
"And of course I am very sad for what happened, but as a team we had a lot of chats, we learned and we had to move on."
Colapinto said he and Norris had since resolved their issues.
"I think he was in the heat at the moment," he said of the McLaren racer's initial comments.
Of Gasly, he said: "Pierre is my teammate and we have a very good relationship as well - so for now, everything is good."
