Tim Husbands said it is also essential that proper transport links are put in place for visitors to reach the site.
He was speaking to the BBC's Inside Business programme about growing Northern Ireland's tourism industry.
Mr Husbands took on the top job at Titanic Belfast a few months before the visitors' centre opened in 2012.
In its first year of operation, more than 800,000 people from 128 countries toured the east Belfast building - double the number it was expected to achieve.
Titanic Belfast welcomed its one millionth visitor in July 2013.
Mr Husbands has a wealth of experience in event management, spending 15 years in charge of Belfast's Waterfront Hall.
He also managed the Ulster Hall and help to stage a number of major events in the city, including the Tall Ships festival in 2009.
In 2014, he was awarded an MBE from the Queen for services to economic development and tourism.
Mr Husbands told Inside Business that, while there is no point creating attractions for the sake of it, parts of Northern Ireland outside Belfast need to be better served in terms of tourism and transport.
"There's no easy means of transporting people through from one city to another, from one region to another, and we need to encourage that," he said.
"You have to make it easy for the consumer, you have to make it easy for the guests.
"I'm not sure that we are mature enough as an industry to do that just yet."
Tim Husbands interview will be broadcast on BBC Radio Ulster as part of Inside Business at 13:30 GMT on Sunday 20 November.
Northern Ireland needs a major new tourist attraction outside Belfast, according to the chief executive of Titanic Belfast.