A 19-12 defeat to France at Eden Park meant England would be heading home early - with the focus immediately on manager Martin Johnson's future.
Johnson is out of contract in December and has admitted he would take a few days considering his own options after England failed to achieve their semi-final target.
However Andrew will hold a root and branch review in to what went wrong in New Zealand.
"The key thing from my point of view is that we take the next four to six weeks with Martin and review what has gone on," said Andrew.
"Martin will reflect on what has happened and why we have gone out in the quarter-final of a World Cup.
"It is very disappointing that it has happened. The important thing now is to take stock.
"We said right from the start that we would take this right through to this World Cup with Martin in charge.
"We have done that and now we will sit down with Martin and look at what has happened.
"It is my job within the RFU to look at the review and take it forward and at some point in the next few weeks reflect and then make a decision.
"We will do that as quickly and as openly possible as we can."
Andrew said the review process would be "robust" but he added there would be no "over-reaction" and no parallels should be drawn with Brian Ashton's departure as head coach in 2008, having guided England to the World Cup final.
"Don't draw any conclusions from anything. We need to look at this review, which we will do, in a very robust manner over the next few weeks, reflect on where we are as a squad, where Martin is in his role, and look to the next few years," Andrew continued.
"Obviously it's very disappointing to go out of a World Cup quarter-final, it's happened before and it will probably happen again to teams.
"We've just got to look at where the squad is, and I think there is a very talented group of young players that have come into the squad over the last 18 months.
"But as we all know you get it wrong in one World Cup knockout game - whether it's Ireland in Wellington who I'm sure will be reflecting the same this morning - you've got it wrong and that's it you go home.
"That's the nature of World Cups, we've all been there before so now we have to take stock, not over-react one way or another, which we won't do."
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