Often - and David did this too - we want to ask God not to just rescue us, but to destroy our enemies. In this psalm we see that David's motivation isn't for his own good, but so that all the world would know that God reigns in Israel. It was for God's glory, not his own.
And then, at the end of the psalm David says,
16 But as for me, I will sing about your power. Each morning I will sing with joy about your unfailing love. For you have been my refuge, a place of safety when I am in distress.
17 O my Strength, to you I sing praises, for you, O God, are my refuge, the God who shows me unfailing love.
This seems like a good way to respond to all of the evil in the world. It's OK to ask God to rescue you. It's best for it to bring Him glory, not just for yourself. And in the end you need to choose to sing with joy about God's unfailing love. Sing His praises.