That's the polite thing to say, without bruising egos or burning bridges. I left my last job because I felt unappreciated after being skipped over promotion, even after accomplishing all the tasks I had agreed to with my manager would give him the capital to push for my promotion. Instead, other members of my team got promoted - and that was the primary reason I started looking around.
The fact that I'd be paid more wasn't the primary reason, few people leave a job for a lower paying one, so it's often an effect, rather than a cause. When asked in my exit interview, guess what I said my primary motivation was? Hint - it wasn't "I'm disgruntled because you didn't keep your end of the bargain"