Who hasn't had one of those frustrating experiences where a big fish gets away and leaves you shaking your head? I certainly have, and occasionally at very bad times.
Although fast action rods in higher line weights certainly help you get your fly out there further it is good to remember that a lighter more supple rod will absorb shock better while fighting fish and will protect tippet and keep flies tightly hooked without pulling them out.
Remember, however, that your rod needs to have enough power, especially in the butt section, to turn a big fish or it actually becomes a handicap. I really like a medium action 8 1/2 to 9 1/2 foot 4 weight for most trout fishing situations with fish up to 18 inches or so.
Soft 3 weights are great for smaller trout and medium 5's for larger ones. In salt water or salmon and steelhead fishing try going down a size for more shock absorbing action as long as you have the power to stop and turn fish.
Whenever possible, don't let fish get downstream or near obstacles and pay attention to the angles that you're using to pull on fish. If you're pulling straight out of the fish's mouth instead of back into the fish there is a far greater chance of the hook popping out.
Pay attention to how the rod is bending as well. Use the butt for more power, the soft tip to absorb shock, and different parts in between depending on the force the fish is exerting. Unless there are weeds or other obstacles, most pros keep the rod low not high, often even putting the rod under water to better absorb shock.
Experiment with different rods and techniques for the different situations you find yourself in and pay more attention to landing fish effectively, it will make for more smiles and more great fish pictures in the end.