England last failed to qualify for a major tournament in 1994

England need Croatia or Russia to slip up in their last Group E games, with their best hope lying with Russia's trip to Israel next month.

Barwick said: "Steve has our support but our job is to focus on Croatia.

"It is a very big day when Russia play Israel on 17 November, we need Israel to stop them winning and help us."

Interview: FA chief executive Brian Barwick

Interview: Former England boss Graham Taylor

He added: "Steve has a job to do and he must now get the players ready for the Croatia game.

"We know we need a favour but it is desperately important that we continue to concentrate on qualification."

McClaren himself refuses to believe his side's hopes of reaching the finals in Austria and Switzerland are over.

"We still have hope, it is not the end," McClaren insisted. "It would be a huge disappointment if we did not get there but we are not even thinking about that at the moment.

"We are in a results business. Now we have to rely on Israel getting one for us.

"We still have one game to go. Russia have two. That is the reality. Let's see where we are after 12 games."

McClaren has been in charge since August 2006, when he was promoted from the role of assistant to Sven-Goran Eriksson, who is now manager of Manchester City.

England played very well and I am as disappointed as anyone Former England boss Sven-Goran Eriksson on the defeat by Russia

The Swede believes McClaren should keep his job, despite the 2-1 defeat in Moscow, which leaves England's hopes of playing in Austria and Switzerland next summer hanging by a thread.

"England still have a possibility of qualifying - and I hope that they will," said Eriksson. "Steve is my friend, I worked with him for five-and-a-half years and I feel sorry for him.

"England played very well and I am as disappointed as anyone. I don't think England deserved to lose. They should have at least had a draw."

The defeat has intensified the pressure on McClaren, who faces the prospect of being the first manager to fail to lead England to the finals of a major tournament since Graham Taylor in 1994.

And Taylor told BBC 5Live: "If Steve does go he will be the sixth England manager to go in the last 17 years, compared with four in the previous 28 years.

"Changing the manager is not necessarily the answer. What we have to look at is our record in international football over so many years. It's poor.

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"I thought it was a great game, fantastic atmosphere but the wrong result. Russia were first class. What they play is a short passing and very swift game.

"We do not play that at international level. That's not in our culture. We've got to look much deeper at what we expect properly and rightly expect from our national side.

"If you look over the years we have not been successful. There is something deeper than just the manager."

Wayne Rooney's stunning first-half volley put McClaren's team in control before a brace from Russian substitute Roman Pavluchenko inside four second-half minutes stunned the visitors.

"It was disappointing for everyone because for 70 minutes we looked in control," added Barwick.

"The game got away from us in four minutes, we went from looking on course for qualification to now needing help from others.

"There are all sorts of twists and turns in qualification campaigns and until the point passes where we cannot qualify, we must go for broke to try to get there."

We need to take it on the chin, take responsibility for where we are and try to win our last game England midfielder Steven Gerrard

However, stand-in captain Steven Gerrard believes England are unlikely to qualify for the European Championship.

"It is looking doubtful," said the Liverpool midfielder. "We will see it out until the end and, hopefully, Israel can do us a favour.

"It was a very shell-shocked dressing room. The players are hurting and down.

"We need to take it on the chin, take responsibility for where we are and try to win our last game."

Meanwhile, Wigan striker Emile Heskey, who was influential in wins over Israel and Russia in September, is unlikely to be fit in time for England's final group game.

He broke a bone in his foot in September and Latics boss Chris Hutchings said: "The scans have revealed that everything went OK and they are very satisfied with the way it has gone but I would imagine that his recovery will be three or four weeks.

"We are governed by the medical staff of the rehab about what he can and can't do.