Football Association (FA) chief executive Martin Glenn wants England to cure their "perennial problem" of being "brittle" at major tournaments on the back of a humiliating Euro 2016 exit.
Glenn spoke alongside departing manager Roy Hodgson in Chantilly after the squad beaten 2-1 by minnows Iceland in Nice in the last 16 on Monday made a sorrowful trudge on to the team bus from their nearby hotel.
Hodgson resigned via a short statement after the match, reiterating "I don't know why I'm here" during Tuesday's press briefing.
Glenn praised the outgoing coach, telling him the Iceland loss should not define his reign, but conceded a pivotal task awaits as he prepares to select a successor with the help of technical director Dan Ashworth and former Manchester United chief executive David Gill.
"It is important we get this right," he said.
"It's important that we make the right decision. We are going to be canvassing opinion from former managers, former players to make sure that we get a lot of wisdom.
"We don't need to throw the baby out with the bath water. There are a lot of good things being done with the England team that we can build on.
"But there is not denying the perennial problem that, at the business end of a tournament - and we are in the tournament business - England seem brittle.
"We need to understand why that is. It's not a particular issue Roy Hodgson's had to face, people before Roy have faced it too.
"It's our commitment to say in future tournaments that every game, every match, every half we will punch our weight.
"We will go to tournaments as contenders and get over this brittleness, where we can hit a banana skin and under deliver against the potential of what is a great squad and a very well-resourced team."
England have alternated between overseas and English coaches since Sven-Goran Eriksson's appointment in 2001, with Hodgson's tenure coming after the reigns of Steve McClaren and Fabio Capello.
Glenn insisted he would not rule out looking beyond domestic coaches once more this time around, but refused to throw any names into the frame.
"We'll be looking for the best person for the job," he said. "I'm not ruling out a non-English coach, the best person for the job.
"I'm not going to talk about names, it's not even 24 hours since we've gone out of the tournament, but I've been consistent in saying we will get the best people to take this exciting group of players further forward.
"We are looking for the best person, not necessarily the best Englishman."
Former England defender Gareth Southgate is the bookmakers' favourite to succeed Hodgson, having guided the country's Under-21 side to glory at the Toulon tournament last month and Glenn insisted that the infrastructure the FA has in place at its gleaming St George's Park base is starting to bear fruit.
He said: "The big reinvestment is still quote new. St George's Park is a bit like a Premier League club opening an academy. You start with putting the various structures in place, getting performances happening. They're not going to break into the first team straight away.
"St George's Park, focusing on the under-16s to all the way through, shows that we are punching our weight in development tournaments - Toulon is a good example.
"You can progress and there are reasons to be cheerful. What we have to do in knit it up to the senior squad."