Proving the higher management the testing has been done properly

As a tester, i often end up in a situation where, i have approved a functionality is working fine. But, when it is moved to production environments, the functionality seems broken down completely/partially. In between i might receive number of builds from developers for various bug fixes. At this point of time, the functionality might have broken on any builds. But, i may not be able to verify each and every time, the complete product for each new build. Ultimately, when a bug is reported in production, the question comes to testing team as "Why is has been missed and how?". The main problem is i might not have the necessary proof to support my claim that i have tested properly or i don't even know in which build this breakage happened.

So, what am i missing here. How to prove that testing has been conducted properly. Also, what should be set as an entry criteria when taking new builds. Please help me on this