How can I prevent water from getting behind the gutter?
Is the water running down the roof not going into the gutter, and instead flowing behind the gutter? If so, then there is a problem with the gutter and/or flashing installation. In addition to the drip flashing, you should check that the gutters are properly affixed. They should be sloped toward the downspouts, but are they securely attached to the fascia board? The fascia board could be rotted, and the gutter hangers unable to hold the gutters firmly against the building. (This is the sort of problem that rapidly gets worse, as the more the fascia board is exposed to water, the more it rots, letting the gutter hangers fail.)

Alternatively, if the gutters are overflowing and draining toward the house instead of down the downspouts, then you probably just need to clean the gutters so they can drain properly.