A 0-0 draw at the Riverside Stadium left the Teessiders still inside the relegation zone with just five games to play, and the next two against Champions League semi-finalists Arsenal and Manchester united.

However, Southgate is refusing to throw in the towel.

He said: "Everybody will look at our fixtures, as we have said for a few weeks, and feel that we are gone, but we are still just managing to hang in there.

"You just don't know what can happen in football, you really don't.

"All the teams we play have got something to play for, so they have got their own pressures.

"The one thing we know is that we are going to fight right through and see where it takes us.

"We would have loved the three points today, but I have always felt we would probably need to go to Newcastle and win, and that looks like it is still going to be the case.

"But who knows what might happen between now and then because we are not just going to sacrifice the next two fixtures.

"We have got to go and try to get something from them, and we have done in the past couple of years."

It might have been so different had keeper Mark Schwarzer not returned to haunt the club he served with such distinction over more than 11 years.

The Australian, who rejected the chance to extend his stay at the Riverside to join Fulham, pulled off a superb 47th-minute save to keep out Tuncay Sanli's header and with it, repel the Teessiders' best chance to break the deadlock.

Southgate said: "It was a fantastic cross from Jeremie [Aliadiere], it was a great late run from Tuncay and a great header, and it was an outstanding save."

Things might have been even worse for Southgate's side had Andrew Johnson's 34th-minute shot not come back off the post, or had Clint Dempsey or Bobby Zamora made the most of late openings.

In the event, the bulk of a crowd of 30,380 left the stadium knowing their club's top-flight status is hanging by a thread with just five games remaining.

However, Fulham manager Roy Hodgson, who guided his side to safety against the odds last season with a remarkable late run, insisted his opposite number could take plenty of positives from his side's performance.

He said: "We had nothing like 31 points at this stage last season - we finished with 36 and we took 12 out of the last 15. At this time, we were somewhere in the mid-20s with five games to go.

"If he wants to take any encouragement from that, Gareth, he is very welcome to do so, but I certainly thought that on the side's performance today, that didn't look to me like a relegation team.

"It looked like a team that's got the wherewithal to get the necessary points to stay in the league.

"But it will be tough. I am afraid that the battle that we have witnessed today and Fulham have taken part in, there will be five more of those battles to come, and he might have to do it against teams in the top four as well, so it won't be an easy task."

Asked about his own team's chances of European qualification, Hodgson replied: "I have said many times UEFA (Cup) has never been an actual target for us.

"But of course, if we continue to play well, maybe things will fall into place and maybe we will get a European spot.

"If we do, we will be very grateful and we will do our best to represent England in the right way."