"They didn't take their chances in their last Group B game against Germany when it mattered most and by the time they realized that, time was against them, the game was already won and lost".
Vargas reacted quickest to obtain the knock down to half-time sub Martin Rodriguez, who scored his first worldwide goal with a sharp surface that soothed Chilean nerves.
Participants in the 2017 Confederations Cup are hosts Russian Federation, 2014 FIFA World Cup Champions Germany, 2015 Copa America Champions Chile, 2015 AFC Asian Cup Champion Australia, 2015 CONCACAF Gold Cup winners Mexico, 2016 UEFA Euro Cup champs Portugal, OFC (Oceania Football Confederation) Nations Cup victors New Zealand and 2017 CAF Africa Cup of Nations Champion Cameroon.
The German said he profited from confusion in Cameroon's defence, which was generated when the ref initially dismissed Sebastien Siani before the video assistant referee corrected the decision.
Cameroon had Ernest Mabouka sent off in controversial fashion on 64 minutes for a risky tackle on Emre Can.
After Kerem Demirbay opened the scoring in Sochi, Werner struck either side of Vincent Aboubakar's consolation effort on 78 minutes.
"We had trouble imposing our style of play", said Chile coach Juan Antonio Pizzi.More news: England U21 v Germany U21
Chile will face Portugal in the last four in Kazan on Wednesday.
At Moscow's Spartak Stadium, the Aussie display was energetic and full of intent throughout, but the result wasn't enough to make the top two in the group, meaning their FIFA Confederations Cup campaign is now over.
"We were just talking about it in the sheds", he said.
"We wanted to continue in the tournament, we wanted to get out of this group".
"They (Chile) are a world class team, a fantastic team, and have played some of the best teams in the world off the park".
Postecoglou praised veteran forward Tim Cahill as Australia's captain made his 100th global appearance.
For the Aussies, head coach Ange Postecoglou made six changes from the team that drew with Cameroon in the week, with Tim Cahill, 37, coming into the team to win his 100th cap - becoming only the second Australian player ever to reach the milestone.