"We also need to demand more of ourselves, as we strive for a Jamaican dream of success in all areas of our lives," he added.
He was speaking during the Independence Civic Ceremony held in the historic Sam Sharpe Square in Montego Bay on Saturday.
The Montego Bay business sector leader, who noted that 49 years is a relatively short period of time in the life of a nation to achieve greatness, also highlighted the outstanding achievements that have been made in such areas as sports, music and culture.
He was, however, harshly critical of the nation for not adequately glorifying the principles and courage of our ancestors.
"We can all agree that we still have a far way to go in honouring the ideals and spirit of our ancestors, who sacrificed so much, in order that we can gather here this morning (Saturday) in such a fashion," Crump observed.
He made note that the celebration of independence is not just about festival songs, street dances and wearing national colours, nor is it about older Jamaicans reminiscing on the lowering of the Union Jack 49 years ago on August 6, when Jamaica declared its independence from Britain.
"Independence should be about a true reflection on where we are as a people, where we want to be and through working together, how we are going to get there. With unity of purpose, all the good things we seek can be realised, and I guarantee you we don't have long to wait for another 49 years to do so," Crump advised.
During Saturday's ceremony, the Prime Minister's Independence Day message was read by JLP councillor Heroy Clarke; while Henry McCurdy, the Opposition People's National Party (PNP) caretaker for North West St James read the Oppostion Leader's message.
Ian Dear, who deputised for Custos of St James, Ewen Corrudos, read the Governor General's message.

