Asian fashion e-commerce start-up Zalora aims to become a multi-billion dollar company, and according to managing director Michele Ferrario, Southeast Asia's burgeoning market holds the key to achieving that goal.

"Singapore is well-served in terms of online and offline retail, but when you think about smaller towns in Indonesia, the Philippines, Vietnam and Thailand, people there do not have the same access to fashion as people in developed markets," he told CNBC's "Managing Asia."