City initially looked in control after Jack Grealish and Erling Haaland scored early in the second half. However, PSG mounted a stunning comeback.
The defeat marks the first time City coach Pep Guardiola has lost four in a row in his managerial career.
Southgate had initially named a 33-man preliminary squad but had to drop seven before the June 7 deadline for countries to submit their final squads.
The 2024 awards ceremony will come up on January 19, next year, in the United Arab Emirates.
Referee Paul Tierney missed the initial incident, but after consulting the VAR screen, he awarded United a penalty, which Bruno Fernandes duly converted.
Haaland watched the encounter from the stand after being sidelined by an injury prior to the last international break.
Manchester City, who knocked Chelsea out of the League Cup late last year, host Chelsea next Sunday in the FA Cup.
England beat Iran 6-2 in their opening Group B match at the ongoing Qatar World Cup on Monday.
It took City just 56 seconds to take the lead at Molineux Stadium as Jack Grealish fired in his first goal of the season.
So far, City have garnered 56 points in 22 games, while Chelsea comes behind them with 43 points in 22 games.
