Speaking at a 'Mad Men vs Math Men' talk at the Advertising Association's Lead conference, Griffith advised companies to "segregate a pool of money to be deliberately inefficient because that is where serendipity happens".
Griffith pointed out brands can create an atmosphere conducive to innovation by setting aside a proportion of employees' time or setting up a project that has no key performance indicators or expectations of a return on investment.
Ronan Dunne, chief executive at Telefonica UK, added that he believes a key contributor to success is putting faith in the brand by placing the marketing director on the board and allowing them to "own" the P&L (profit and loss statement).
He said: "Before you can sell a brand concept effectively to customers you have to sell it in the board room and there are not many representatives of the marketing industry who are actually sitting in the board room."
Building up the "integrity" of the brand in the board room is possible by ensuring CEOs can have confidence in the metrics driving the business relate to brand, argues Dunne.
Griffith believes media owners such as Sky should shoulder some responsibility for providing marketers with the ammunition they need.
He said: "It is up to us as media owners to be equipping you with all the tools to make that case in the boardroom.
"Something like AdSmart is hugely measureable and transforms the debate about reconciling inputs and outputs."
Marketers should be in another job if they do not have a "super clear granular view" of customers, according to Griffith.
He said: "It has to be super granular otherwise it is no longer insight because there is someone out there who can have more granularity than you have.
"I think the reason Sky is successful and marketing is at the heart of our business is because we have a one-on-one customer relationship. That is the way the world is going with people who have grown up with digital technologies."