Look at this definition of begin from TheFreeDictionary.com:
- To do or accomplish in the least degree
Those measures do not even begin to address the problem.
It talks about an action/thing being so hugely dramatic that something else said or done in return almost pales in comparison to it, so it doesn't even begin to solve the problem.
For instance, if you have done a grave mistake, or a terrible sin, and upon realizing your mistake, you say "I'm sorry", you might get a reply:
Sorry doesn't even begin to cover it
Sorry doesn't cut it
I cannot give you an exact answer on your quote without the context, but "Okay doesn't even begin to cover it" is also used in a similar sense here. The key point to focus on is "doesn't even begin".