But here are some random thoughts:
1) It helps to have a "top heavy" pitching rotation, i.e. a solid SP1-SP2-SP3. Depth at SP4 and SP5 is great during the regular season, but provides little value in the post-season as you rarely would need to go to your SP4 and never to your SP5.
2) Turn off auto-rest for your position players in the post-season. They can rest in the off-season.
3) Keep in mind, you are playing other good teams in the post-season. Your series' are more likely to be evenly matched, so "random luck" may play a larger role in the post-season than it would during the regular season.
4) If you have a top-quality minor league prospect who's ML ready, but you've been holding them back for next season, don't be afraid to put them on your playoff roster. I've had a number of players make their ML debut in the playoffs. They don't accumulate any service time during the post-season, and if they are better than a corresponding player on your regular season roster, it's basically "free" to put them on your post-season roster. You just have to make sure they are on the 40 man roster before the "set post-season roster" date during the regular season. At worst, you burn an option year.