He wishes he didnt do it. Wrong.
He wishes he hadn't done it. Right
He wishes now that he went to Italy. Wrong
He wishes now that he'd gone to Italy. Right.
However, the form with the simple past is possible, but it means something different. The following are examples:
He wishes he didn't bite his nails. (But he does).
He wishes he went to Italy more often. (But he doesn't)
He plays a lot of poker. He wishes he won the game more often. (But he doesn't)