How to get sweat smell out?

I have problem, and am super embarrassed about it. Thank god for this forum of trusted friends who will not judge me. (Don't judge me!)

I just purchased a brand-new office chair for my home —one of the black ones with the mesh-type material that you would see at any office. One day, after I finished my workout, I sat down on it to answer some quick emails. I noticed afterward that the chair then reeked of sweat.

I tried to clean it a little with all-purpose cleaner, but I'm still smelling the sweat smell when I sit in it. I have no idea how to clean a chair like this — any tips? Does anyone know how to get the smell of sweat out of something? Ugh, I'm so gross.