I think there is a connection, but there are important differences.

First, envy is a different issue than complaining. People are complaining every day, which is mostly a good thing, because it encourages improvement and self-critism. Think of inventors or human rights fighters. However, envy is almost always a bad thing that shouldn't happen too often. It causes anti-social behaviour and thus must be fighted against.

Second, poverty is not the opposite of wealth, it's the other extreme. Also, wealth means more than just material wealth, and this extended meaning is essential to the saying I cited above. In contrast, poverty means material poverty, which is kind of misleading in the context above.