What's the penalty for Synthetic methods?

While developing a Java application under Eclipse I got the warning about "method/value accessed via a synthetic method". The solution was simply changing a private access modifier to a default level.

That left me wondering: what's the penalty on using a synthetic method? There is some? I assume so as the compiler/Eclipse raises the warning, but it's something so relevant or something that could be safely ignored?

I've not seen this information around here, so I'm asking.