Is drawing resources required?
You must draw all of your goods.
From the FAQ:

Resource Cards - Can I voluntarily take less resources or none at all after the production roll?
Answer
No.

I don't believe there is any official guidance on what to do if draws are forgotten about.  If it is noticed fairly quickly, the draws should be made up.  But if you've gotten to a new round of trading, or a 7 has been thrown, it is probably too late.
You can consult this past question that gives general advice on Take Back Privileges that might be helpful in resolving the situation.
The answer stays the same for Cities and Knights