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Addressing fans at a concert in Chicago on Friday night, the singer also thanked them for continuing to support him.
The 43-year-old pop star was arrested in New York on Tuesday for running a stop sign and failing to stay on the right side of the road.
His lawyer has said he looks forward to vigorously defending the singer.
Reports say the arrest occurred in Sag Harbor in the Hamptons, a popular summer destination for celebrities on Long Island.
He was released without bail after being formally charged, and is scheduled to appear virtually in court on 26 July.
Suffolk County District Attorney’s Office has said Timberlake has previously spoken openly about seeking help for excessive drinking.
Timberlake has been touring the US to promote his sixth album, Everything I Thought It Was, and is due to launch the international leg next month, kicking off with a two-night run in Poland.
His scheduled court date coincides with the start of his world tour at the Tauron Arena in Krakow.