Sam Allardyce delighted that Sunderland's destiny is in their own hands

The Black Cats clambered out of the Premier League’s bottom three after their third clean sheet in the last four matches enabled them to take a point from an Arsenal side that remain in the Champions League places.

Sunderland are above Norwich on goal difference and a point clear of Newcastle ahead of their final four matches, which will see them face Stoke, Chelsea and Everton before travelling to Watford on the final day of the season.

Their recent form is good enough to suggest survival is in their grasp, and today’s point means they do not have to rely on other results provided they pick up sufficient points themselves.

“Our destiny is in our own hands now for the first time in many months,” said Allardyce, who watched Sunderland come closest to a breakthrough when Patrick van Aanholt struck the woodwork with a first-half free-kick. “We’ve got to take full control of that, starting at Stoke. And when we finish against Stoke, we’ve got to make sure we’re still out of the bottom three.

“It was another clean sheet and a very, very good point. For the first time for many, many months, it moves us out of the bottom three, albeit on goal difference. Psychologically, that will hopefully be a big boost for the players.

“For me, another clean sheet is where our safety really lies. We need to keep as many clean sheets as we can. We’ve done really well recently and that's helped us claw our way out of the bottom three. We've got to try and get another clean sheet next week.”

Since dropping back into the bottom three at the start of last month, Sunderland have lost just one of their last five matches.

They are handling the pressure of the relegation fight, and are arguably playing as well now as at any stage of the campaign.

Defensively, they look rock solid, with Lamine Kone and Younes Kaboul forming an effective centre-half partnership and Jan Kirchhoff continuing to provide a reassuring presence in front of the back four.

They failed to make an attacking breakthrough today, but as well as striking the woodwork through van Aanholt they also forced Petr Cech to make three excellent second-half saves.

“I’m really pleased with the level of performance under the pressure we're under,” said Allardyce. “I was pleased we overcame our nerves and started to pass the ball properly in the second half.

“When we passed the ball properly we caused Arsenal all sorts of problems, and for 90 minutes we defended superbly well.

“I thought we paid them a bit too much respect in the first half, but we sorted that out at half-time and were much better. We got in the faces of their midfield players and stopped them playing through midfield. We caused a little bit of panic in the Arsenal defence and I was hoping we would score in that period, but unfortunately we didn’t.”

Allardyce felt his side should have had a first-half penalty when Per Mertesacker blocked Jermain Defoe’s shot with his hand, although Arsenal might also have had a spot-kick when Alex Iwobi’s shot struck DeAndre Yedlin on the arm.

“The referee should have given us a penalty,” he said. “It was obvious for me. He turns his back and sticks his arms out. When you're trying to block a shot you're not supposed to turn your back. It stops a certain goal. For me it was 100 per cent a penalty.”

Arsenal boss Arsene Wenger felt the result represented two dropped points, and while the Gunners remain five points clear of Manchester United in the battle for the final Champions League place, he admits there is little room for manoeuvre with Louis van Gaal’s side boasting a game in hand.

“We care about that and we worry about it as well,” said Wenger. “It is a fight, and there are two leagues at the moment. There are teams that are taking it easier and you see that in some games.

“You think, ‘I would like to play them now’ – the teams that are safe and do not go for Europe. Then, you have teams that go for something at the top and the teams that fight not to go down. It’s different games.”