The Frenchman was in an offside position as the Ivory Coast international's piledriver flew past helpless keeper Joe Hart, although Pardew could not accept Mr Jones' judgment that he was interfering with play.
He said: "I have gone and seen him. I was right behind the shot, as the fourth official was, and it was a clean strike.
"It was a great moment for this football club to get a goal like that, so if you are going to chalk it off, you need to make sure that you are getting the point right.
"My point was did he think Gouffran was interfering with Joe Hart, and he said, 'He was in the six-yard box', and I get that.
"The guy was recovering from an offside position, he didn't want anything to do with the play, but he is not interfering with Joe Hart's vision. In fact, it goes on the inside of him.
"The Man City players are impairing Joe's vision, not Gouffran.
"It's a real technical matter that he's talking about here, and to chalk a goal off of that quality, that takes some doing, I think, and it did set the tone for the rest of the game.
"I think if you are going to call a guy retreating from an offside position, it has to be pretty clear that he is interfering with the goalkeeper's view.
"The linesman, even though he was on the wrong side, couldn't have been clear on that, and the referee definitely couldn't have been clear on that."
However, Manuel Pellegrini was confident that the referee, who consulted assistant Stephen Child before making his decision, had got it right.
He said: "There was a player offside when the other player kicked the ball. It was offside and was perfectly not valid at all."
City had taken an eighth-minute lead when Edin Dzeko converted Aleksandar Kolarov's left-wing cross, but they had to wait until the fifth minute of stoppage time at the end of the game for Alvaro Negredo to seal victory with his 19th goal of the season.
Pellegrini, whose side leapfrogged Arsenal into first place as a result of their win, said: "It was a very big result because it's a very difficult stadium to play here. We, Chelsea and Manchester United know how difficult it is to play Newcastle.
"They have a direct style with a lot of physical power, and the whole game, they were trying to score with crosses and shooting, and we were very concentrated in defending.
"Also, we scored two goals and we had two or three more clear chances to do it."