Yeah, epsxe should handle your controller fine. Make sure you'r going "CONFIG > GAMEPAD > PAD 1" and then selecting each button and defining them to be an action on your gamepad. If this isn't working at all - make sure your pad's drivers are up to date from your manufacturer.
A little problem I seem to have now and then is that when I define a button on my usb pad it automatically returns it back to being the default keyboard value when I switch the focus to another field. But, what seems to fix it is enabling "CONFIG > GAMEPAD > MULTI-TAP", re-defining the buttons for PAD 1 and then turning MULTI-TAP off. I'm not sure if anyone else has ever had that problem... could be just me.
None the less try what I said and let us know how things pan out.