Here's the Cambridge University Press Idioms Dictionary definition:
A penny saved is a penny earned.
something that you say which means it is wise to save money
It is often used to encourage people to be careful with their money, where their would be no notion of the respect you refer to- quite the opposite in many cases. When people say it when they haven't spent something, they might be pleased with themselves, but I believe that the underlying concept of the idiom is about thrift and avoiding waste rather than about respecting yourself for doing it.
