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Turns out, getting pulled over for speeding with an open bottle of vodka in the car -- and admitting you'd fail a drug test -- does not go over well with your boss.

At least, that's the takeaway from Jimmy Haslam's comments about Kareem Hunt -- with the Cleveland Browns owner ripping his running back over that Jan. 21 police incident.

"What he did was not acceptable. He's got to do better," Haslam said Wednesday ... "It's not good. Kareem knows he's got to do better."

FYI, Hunt is now a restricted free agent -- and after watching the clip, you gotta wonder if the Browns are just gonna cut bait with the guy considering his controversial past.

Haslam said there's still a chance they keep Hunt around for one more season -- but even if they do, he's clearly on super-thin ice.

As we previously reported, Hunt was pulled over for speeding in Rocky River, Ohio -- and during the stop, cops say they found weed and an open bottle of vodka in his ride.

In police footage, obtained by TMZ Sports, you can see the pullover was not the best look for Hunt ... who straight-up admitted he would have failed an NFL drug test at the time of the stop.

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Hunt was issued a citation for speeding ... but he was NOT cited for the pot -- and was sent on his way by the officer.

Haslam was asked about the incident during a press conference announcing the team's new GM ... and his disappointment in the 24-year-old was palpable.

"We have and will continue to work closely with Kareem," Haslam said. "But he knows our expectations are higher than what he showed a week or two ago."