Keep mana pots on you and some mana drink. I think that shadow priests do great damage when geared well, and played correctly.
This. Their damage is pretty decent honestly. Absolutely NO burst, so you HAVE to stack crit and rely on crits for any kill potential at all. BUT, people absolutely cry and go nuts if you don't bubble and heal them, but what they don't understand, is that if I dot 3-4 people, bubble myself, fear/root people off me, I'm half mana already. The ONLY way to play Shadow is to be VERY greedy with heals and bubbles, and only use them on yourself. Otherwise you last 10 seconds in a fight.