Chelsea's Pochettino backs Sterling to prove Southgate wrong after England snub
The west London club secured back-to-back league victories for the first time since March after coming from behind to thrash promoted Burnley 4-1 on Saturday and move up to 11 points.
Sterling had a hand in all four of Chelsea's goals at Turf Moor, including scoring the third.
Southgate has not called up Sterling for the friendly against Australia and 2024 European Championship qualifier versus Italy later this month.
"He did well; he was involved in all the goals, and I'm so happy for him and for the team," Pochettino said. "The team was good, the performance was fantastic, they deserve all the credit.
"I think a player with his experience knows he needs to perform and to show the manager of the national team he was wrong in the decision.
"Only with performances and scoring goals is he going to show he deserved to go."
Sterling, who made his international debut in 2012, has scored 20 goals in 82 appearances for England but has not been picked since their World Cup quarter-final exit in Qatar last year.