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He added that his resignation will be effective in seven days.
Acosta has served as the U.S. secretary of labor since April 28, 2017.
"I think he was a great labor secretary, not a good labor secretary," Trump said Friday. "He's done a fantastic job. He's a friend of everybody in the administration."
Trump said he thought Acosta did a "very good job" earlier this week while explaining the circumstances surrounding the 2008 nonprosecution deal reached with Epstein while Acosta was serving as the U.S. attorney in Florida.
"He explained it," Trump told reporters Friday. "He made a deal that people were happy with and then 12 years later they're not happy with it."
The deal, which has come under renewed scrutiny since federal authorities revealed new sex trafficking charges against Epstein on Monday, allowed the 66-year-old to avoid significant jail time and federal prosecution after he was accused of molesting teenage girls.
Acosta defended his former office at a news conference Wednesday and claimed federal prosecutors only stepped in because state prosecutors planned to drop the case against Epstein. Former state officials involved in the case have disputed Acosta's account.
Federal prosecutors in New York on Monday unveiled new charges of sex trafficking and sex trafficking conspiracy against Epstein. He is accused of molesting dozens of teenage girls in Florida and New York between at least 2002 and 2005.
The Associated Press contributed to this report.