Developers MUST test their work. It is an implied responsibility.

I'm assuming you don't have a team dedicated for doing the tests based from your statement. However, having a team dedicated for testing will really help as developers tend to test their code the way they coded it. It doesn't mean that once you have a quality assurance team of some sort, you already can take out testing as a responsibility of the developers.

Developers usually use nets with huge holes for catching bugs. As a result, smaller bugs escape.