A finished first draft is like a freshly baked pie. When you first take it out of the oven you have to put it on the rack to cool. If you try cutting a piece hot, it falls apart, the insides oozing out as you attempt putting the piece on a plate. If you try tasting it, your tongue gets burned.
It's mysterious how this works, but distancing yourself from a finished first draft is absolutely essential. The degree of objectivity gained with even a few days of cooling off helps enormously as you go back to appraise what you've come up with.
More often than not, when you finish writing that final page, that negative voice will have grown from a whisper to a shout. However loud it may be, resist concluding that what you've written is terrible. Realize these feelings are normal. There’s also the outside chance the opposite may happen and you're so excited about what you've written you can barely contain yourself. Or you may be somewhere in the middle, uncertain as to its merits.
Whatever your feelings are toward that stack of pages, however, the worst thing you can do is to immediately start reworking them. You need, instead, to put your newborn draft away and totally forget about it for awhile. Two weeks to a month will permit you to gain some distance, but some writers need much more time. During this break try to engage yourself in some other all-consuming project, perhaps even starting work on another play. Or, as Marsha Norman suggests, "You should just find wonderful things to read between the time you put the play away and the next time you pick it up. You should fill your mind up with other language, other characters' concerns."
I also highly recommend that you still don't share your work with anyone else even though the urge to do so now that you have a completed draft is often compelling. During this cooling off time you and your play are still incubating together. It should still be a private process. Getting input from others now could forever destroy that special, intimate, personal relationship you've been nurturing. So fight off the impulse to share your play quite yet. You'll be happy you did when you come back to it.
Usually what happens when you return to your draft after such a distancing period is that it'll surprise you. If you hated it when you put it away, now it'll most likely read better than you thought it would. If you loved it, now it'll probably be obvious that it needs more work. The point here is that your ability to judge its merits can only really be trusted if you've allowed yourself to gain some objectivity and the only way you can achieve that is to put it on the rack and let it cool off for a while. I've never encountered an exception to this.