There's a difference between shy and reserved.

Here are the relevant definitions from Dictionary.com (since we are talking about our modern interpretations of character, I don't think we need to consult a 19th century dictionary.)

Shy
1. bashful; retiring.
2. easily frightened away; timid

Reserved
....
3. formal or self-restrained in manner and relationship; avoiding familiarity or intimacy with others

The shy person lacks the courage to engage with others. The reserved person lacks the will to do so.

I cannot recall any evidence that Darcy lacks courage, but we do see that he lacks the will to engage at several points. At the Meryton assembly: I am in no humor to .. give consequence to young ladies slighted by other men. And at Rosings when Col. Fitzwilliam says He will not give himself the trouble.

I, for one, think Darcy is reserved and introverted, but not shy.