The candidate that gets hired is a “best fit” not a perfect fit.
No candidate fits all job requirements perfectly. The best you can hope for is that your background, skills, and experience fit the job requirements better than you competition and there are fewer and smaller gaps. The hiring manager is probably aware of your background/experience/skill/ gaps so denying or avoiding them will only make you look untrustworthy or evasive.
It is a good strategy to mention your areas of weakness relative to the position proactively rather than hoping the hiring manager will not bring them up. Doing so will help you come across as more trustworthy and you will be more persuasive when talking about your genuine strengths.
When using this strategy, refer to weaknesses that the hiring manager is either likely to discover on his own or a weakness that is minor in nature and will not impact your performance on the job. For example, if you are a terrific sales person but have not worked in a specific territory, mention it along with your success strategy for the territory. Obviously, the hiring manager knows you have not worked in the territory and mentioning this proactively will make you look more confidant and trustworthy. Another example, mention that you are not proficient in a certain computer program that is not critical to success on the job. This will also help you be perceived as trustworthy.
If there is a potential “show stopper’ a weakness that may be so critical to the job that you may be excluded from consideration it is not a good idea to mention it. By this I am not referring to a weakness that will prevent you from doing the job (if you have that critical a weakness, do not take the job you will be either unhappy or fired). I am referring to a weakness that may leave the hiring manager seriously questioning you can do the job when you are confidant that you can.
Winning the interview and landing the job is dependent on the hiring manager believing you can do the job and that you are likable and trustworthy. By proactively bringing up a weakness you will be seen as open, forthcoming and trustworthy.