The visitors blitzed to a three-goal lead inside 64 minutes thanks to a Kendall Waston double and another from Ronald Matarrita.
Chile clawed their way back into the game through Sebastian Vegas' 70th-minute strike.
But Sanchez, who was dropped for Manchester United's 3-1 loss at City on Sunday, wasted a golden opportunity to turn up the heat by failing to convert his 82nd-minute spot-kick.
United's out-of-form striker did manage to find the net in injury-time but the hosts ran out of time to get a third.
Sanchez, 29, is at his lowest point since signing for United in January, and a missed penalty will do nothing for his confidence.
SunSport exclusively revealed the ex-Arsenal star threw a dressing-room strop after the Manchester derby in a fury over not making the starting XI.
And Sanchez was reportedly "acting weird" after joining up with the Chile squad for last night's match against Costa Rica and Wednesday's clash against Honduras.
He was said to have been "silent for over an hour" and sat alone on a training pitch while his team-mates played football tennis nearby.
Former Arsenal boss Arsene Wenger reckons Sanchez's poor form is down to a loss of confidence.
SANCHEZ'S REAL DEAL
ALEXIS SANCHEZ has been "offered to Real Madrid" as he desperately touts himself around for a move away from Manchester United, according to reports in Spain.
Los Blancos are in the market for another forward with the former Barcelona star potentially on the move.
Sanchez, 29, revealed he feels alone at Old Trafford earlier this week and still struggles with the language barrier in England, despite his time at Arsenal.
David De Gea, Juan Mata and Romelu Lukaku are thought to be Sanchez's only close pals at United – and the Chilean is now leaning towards a January move.
The Frenchman said: "I believe he has lost confidence. The strength of Alexis Sanchez is to take the initiative, to dribble.
"Those are the players who are most vulnerable when they lose confidence their game is based on that and having that feeling to take initiative, he has lost that slowly.
"Since the start of the season he had a high level of physical energy but he has lost that as well."
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