Starbucks CEO Howard Schultz, speaking yesterday at TheWrap‘s conference on media and the entertainment industry, TheGrill, discussed the coffee purveyor’s efforts in the digital space and how important it is to connect with customers through social media.

“If you give a customer an understanding of what your values are, and they share those values, and they believe it, they will pay a premium,” he said. Schultz also said the company was slow to get on their social media game. However, they’re now leaders in the space and just introduced a new contributor to its upcoming in-store digital network, documentary filmmakers SnagFilms.

“It has become paramount that brands understand that trust isn’t something you build through traditional marketing,” Schultz added. “You do that through integrating social and digital media. It is a science – as well as an art – to understand how to do this in a way that is authentic and genuine, and not just marketing.”

Starbucks VP of digital ventures Adam Brotman also spoke with Mediabistro about the new digital network, and will be speaking at the Think Mobile event in San Francisco tomorrow. Click here for more.