The two sides drew 1-1 at St James Park on Sunday.
The two sides met at St James Park on Sunday afternoon, with both in desperate need of a win to move clear of the relegation zone.
It had appeared all three points were going to be the Black Cats after Jermain Defoe opened the scoring, before a late header from Aleksandar Mitrovic saw both sides share the points.
The result suited neither side as a point apiece left them both in the bottom three, but Souness says that the Magpies will be happier than their rivals with the outcome.
"Both of them still have an enormous job to get out of the mess they're in," he told Sky Sports.
"Sunderland leave St James' feeling sorry for themselves. They had the three points and lost it.
"Newcastle finished the game with their tails up and their never-say-die spirit kept them going and got them a point. The happier team will be Newcastle."
One team who will have been pleased with Sunday’s result is Norwich City as it proved a serious boost to their hopes of avoiding the drop.
They beat West Bromwich Albion on Saturday and the result at St James Park now leaves them three points clear of Newcastle and two from Sunderland.
That is not an insurmountable gap by any stretch of the imagination, but with the Magpies in particular struggling for form, it will certainly given Alex Neill’s side confidence as the season concludes.