The Rugby Football Union will soon begin the search for a successor but Andrew, the director of elite rugby, insists they will not rush into making an appointment.
Equally pressing is the need to tackle the shortcomings of the structure of English rugby which Robinson blamed for the world champions' slump in his departing statement.
Andrew agrees urgent action is required with a long-term solution necessary to stop England - who lie seventh in the world rankings - falling further behind their Test rivals.
He said: "There is no doubt that there is a fundamental problem in the management of elite players.
"This is being highlighted by what other countries are doing, particularly Ireland and to a degree Wales.
"Two countries at international level that are struggling with their systems are France and England. We all know that, we all recognise that.
"The skill is finding the solution long-term and it needs to be a long-term solution, not a case of putting some more sticking plaster on the problem.
"I think what we've probably seen in the last month is that the last of the sticking plaster has come off.
"We can't have another sticking plaster solution to this because it just doesn't work. Long-term is what this is all about.
"When I took the job three months ago I know that some of the issues that came up over the following two years would be important to the future of the English game.
"That was one of the reasons I took the job and now England's problems on the pitch have brought forward that agenda.
"It's clear from the last two or three years that England have been left behind in the world game.
"Our structures have allowed other countries to leapfrog England in terms of player preparation. That's obvious to everyone.
"We have to find a solution to a problem which has been ongoing throughout the 10 years of professional rugby. It's about the next 10 years, not just the next month."
Andrew has given no indication whether a successor to Robinson would be appointed in a managerial or coaching capacity, but he ruled himself out of taking a more hands-on role.
He also stressed the jobs of John Wells, Brian Ashton and Mike Ford - who are forward, backs and defence coaches respectively - were safe.
He said: "We want to calm everything down in the next few months. John, Brian and Mike have only been in place for six months.
"From a management point of view I think we have had enough upheaval in the last six months and we would probably want to avoid any more."