Craig Bellamy, returning to the starting XI for the first time since his knee operation, gave Newcastle the advantage but Stead pounced late on to dent The Magpies' charge for fourth place.
Souness felt his side shaded the encounter and were deserving of their late equaliser.
"I think we played well in the first half and were unlucky to go in 0-0," said the Scot.
"They were always going to be more aggressive in the second half, because we had them on the back foot and won the midfield.
"We conceded a scrappy goal, but credit to my players they battled away and got a deserved equaliser and I felt over the 90 minutes we just about shaded it.
"We have bossed the game for long periods and deserved to get the point.
"If you are a paying customer you want to see your players giving 100 percent and I would like to think the fans have gone home reasonably happy tonight."
Stead performed well and Souness feels he can be a real success in The Premiership provided he continues to work hard.
"It was a difficult pitch on Saturday and it became an aerial battle but tonight on a good pitch we played better and it suited his game better," Souness said of Stead.
"He has got a great goal and when the cross came in from Paul Gallagher he showed real desire to score from an acute angle.
"I am not getting carried away but what he has brought to the team is a work ethic and his running can put some other players to shame.
"It is early days but if he continues to work hard then he can only improve."
