Tony Allen pleaded with cops to hear him out during his drug arrest ... insisting he had nothing to do with "all the extra s***" officers found in the vehicle he was riding in on Wednesday.

TMZ Sports has obtained the bodycam footage of the ex-NBA star's run-in with police in Arkansas ... which shows an emotional Allen insisting the alleged cocaine discovered in the whip was not his -- and an incident like this would torpedo his image.

When the cop initially pulled up to the car, he asked Allen and the driver if either had weed on them or had smoked in the vehicle recently. The driver admitted he sparked up in it the night before ... and his grinder might have some flower in it, although he wasn't sure.

Once 6'4" Allen -- wearing a Grizzlies hoodie and sweats -- got out of the car, t

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