The fact that everything we undertake will fail to produce the results we hope for is not a reason to do nothing. Far from it. The mistake we sometimes make is doing only those things we imagine will make a difference. When that is the case, our motive—the thing the drives us—is change. If change doesn't happen, or happen in the way we expect, we have no recourse but to fall into a funk. But there is a more excellent way.
That is the way of love, or more particularly, loving obedience. Jesus doesn't call us to make a difference in the world, let alone to transform the world. In the Sermon on the Mount (Matt. 5:13-16), he does tell us that we will be "salt"—that is, we will preserve the world from complete self-destruction. No small thing that, but hardly world transformation. He also tells us we will be "light," that is, we'll help people see his truth. But when people see truth, often only hardness of heart sets in. Or worse: hostility erupts, and the bearers of the light are thrown into prison and killed, and the recipients of light remain in darkness.
Salt and light—that's about the extent of our effectiveness. Nothing about transforming the world through our efforts. Make no mistake: Jesus does indeed call us into the world to do stuff: preach, baptize, teach, and heal. But he does not promise results. Faithful diligence in such tasks will sometimes change lives and change communities. Whenever this happens, we can rejoice that God has permitted us to see him at work! But a lot of times when the church has obeyed faithfully, we've only received hardship—violence that seems to make things worse for victim and perpetrator alike.