There are two key differences between practice and important matches: Psychological and Variation.
Psychological. There is little pressure in practice, and so players are loose, both mentally and physically. However, once a game begins, it's easy to get nervous and tighten up. RELAX! Of course, that's easier said than done, especially in a tournament or league match. A great way to prepare for this is to drill as if it were a match. Even if you are doing a simple side-to-side footwork drill, think of it as a match, where you must outlast your opponent, in this case your practice partner. Table tennis is a competitive sport, and to prepare for competition you must do competition.
Which leads to another way of preparing for important matches - practice matches. There's a lot less pressure when you play practice matches, but remember that practice is just that - practice. And so they are a perfect time to practice your mental game. Pretend it's a serious match. Before the point begins, blank out your mind, and just let the shots happen. (Between points is when you think about tactics; once the point begins, you have to just let them happen naturally.) Don't worry about winning or losing practice games; just play your game until it becomes comfortable. Then do the same in tournaments and leagues, where you also shouldn't worry about winning or losing, which only puts more pressure on yourself. The more you do this in practice the easier it will be to do so in important matches.
Always remember that you have your best chance of winning if you don't worry about winning. If your goal is instead to play your best, you will maximize your chances of winning.
Variation. There is much less variation in practice drills than in a game. Most practice drills are somewhat predictable, and so you get balls you are comfortable with. For example, you might do a drill where you serve backspin, your opponent pushes it back to your backhand, and you loop (forehand or backhand). The range of variation in the pushes you'll be looping (amount of spin, speed, height, depth and placement) may be rather small. Drills like this are good to develop your shots, as are pattern drills where you practice footwork.
But in a game, when you serve backspin, your opponent's pushes will vary more. He may push to your forehand or backhand, or short, or he may even attack the push. He may vary the spin more. So you usually have to deal with a lot more variation in a game than in practice, and so it's more difficult to prepare for or react to the many different returns.
How do you learn to react to variation in games? By incorporating that variation into your practice routines. Do drills where your opponent varies his returns. For example, the drill might be where you serve backspin, your partner pushes deep anywhere, and you loop. Or your partner may have the choice of pushing short to the forehand or long to the backhand. Or he may just push anywhere, long or short. When you are comfortable against all these, then you may go for bust, and have your partner return serves any way he wants, including attacking them. (Perhaps serve short so he can't loop, and serve low so he can't flip too effectively.)
All drills can be turned into random drills that incorporate variation. For example, instead of hitting forehand to forehand (or forehand loop to block), once you are warmed up have your practice partner move you around randomly on your forehand side. Or have your partner hit the ball randomly to your forehand or backhand (or to anywhere on the table), and you return each shot to one spot. Or do drills that combine variation with pattern play. For example, your partner may alternate between one shot to your backhand, and one random shot that goes anywhere.
Of course, the ultimate drill that incorporates all variations is a practice match. Play them like tournament matches (though sometimes you should focus on something that needs practice), and they will prepare you for the big matches. Ultimately, to play in games as well as you play in practice, you need to play lots of games - but only after you have really practiced against variable shots in practice.