Although your explanation isn't entirely wrong, It isn't necessarily the backward tilt of the wing, but the backward tilt of the aerodynamic force.
I look at it from two different perspectives. The airfoil is designed to accelerate air thus creating the pressure differentials that make the plane fly. The higher pressure areas will try to push the wing toward the lower pressure areas. The overall sum of these forces is called the resultant force.
That resultant force will have an amplitude and a direction or vector associated with it. The goal of designing an airfoil is to orient those forces upward to counteract gravity. So the designer will make the low pressure areas on top of the wing and the high pressure areas on the bottom to make the vector point upward. A perfect airfoil would create a vector pointing directly upward, 180° from the ground and 90° from the direction of travel. In reality, nothing is perfect, so that vector is always pointed backward to some degree. So we break that resultant force into two components. The part we're trying to accomplish, which is 90° from the direction of travel is called lift and the remaining part which is 180° from the direction of travel is called the induced drag since it is induced by the creation of lift. Even a wing producing lift at a 0° angle of attack will still produce a certain amount of induced drag.
Now we come back to your explanation. Although any time a wing is producing lift it will also produce some induced drag, as you increase the angle of attack the vector of the resultant force tilts back with it. Not necessarily at exactly the same rate, but usually not far off. Since we are still defining lift as 90° from the direction of travel and drag as 180° from it, the ratio between the two changes. For every bit of lift produced there is a lot more drag the further you tilt the wing back.
The second way of looking at it is from the inertia point of view. The intent of the wing is to accelerate air downward. Once again, a perfect airfoil would accelerate the air straight down, but in reality it will always accelerate it slightly forward also. And as you tilt the wing backwards you will produce more forward movement and less downward.