Jackson was commenting on the Acas guidance released yesterday, which provides legal guidance to families and employers who will be engaging with the new form of leave.
Figures from the Department for Business, Innovation & Skills (BIS) suggest around 285,000 working couples will be eligible to take advantage of the benefit from 5 April 2015.
From this date working couples will be able to share the 52 weeks of maternity leave and 39 weeks of pay that the mother is currently entitled to.
Jackson told HR magazine that even though some of the details of these arrangements can "seem horrible", employers should not bury their heads in the sand.
"To the employers I would say 'don’t sweat the details and don't panic'. By the time employees come to you with the forms the decisions will actually be fairly simple. There is plenty of advice out there for employees and employers alike."
Acas head of information and guidance Stewart Gee added that the organisation has worked with employers, unions and family groups to help everyone understand shared parental leave.
"We advise employers and employees to start early with discussions to ensure that they can agree the sort of arrangements that work best for business and families," he said. "We are also running training courses to help employers prepare for the legal changes."