Are you using 4.3.6?
If so, no, this definitely should not be happening. I can play it with D-pad controls just fine.
Did you start the ROM with the X (Cross) button, or with the Triangle button? Because if you did the latter, it's no wonder it will not work - enabling multitap on non-multitap compatible games causes problems.
But even loading it with the Triangle button (which sets up controller port 2 as the Multitap port), it still works with the D-pad button - although I'm skipping straight to a savestate.
So no, it should work with the D-pad.