Newcastle midfielder Tiote thought he had cancelled out Alvaro Negredo's opener when he cracked a stunning 22-yard strike past Joe Hart.
However, the goal ruled out after referee Mike Jones consulted with his assistant Ron Ganfield and decided that the offside Yoan Gouffran was interfering with play.
Gallagher, who refereed in the Premier League for 16 years, told Monday View that the officials had erred in disallowing the goal.
"Jones' first priority would be whether the ball touched Gouffran," said Gallagher, "and from Ganfield's position, he would not be sure. I can understand why he called him over.
"The minute Ganfield said that the ball didn't touch Gouffran, the second question would be whether he is line with Joe Hart.
"It's an afterthought from Hart - he puts his hand up after the ball has flown past him. His last resort is to appeal for offside.
"For me, that's a goal and a mistake by the officials."
Gallagher also felt Mapou Yanga-Mbiwa should have been sent off for his challenge on Samir Nasri, but believed the fourth official sufficiently dealt with the touchline spat between managers Alan Pardew and Manuel Pellegrini.
"Martin Atkinson, who is the one of the best referees in Europe, was the fourth official," said Gallager. "He acted as peacemaker and tried to calm things down.
"The fact you have someone to do that on the line aids the referee no end. I don't think referee would have any concerns about that situation."
There was further controversy on Sunday afternoon at the Britannia Stadium, where Liverpool were awarded a second-half penalty after Raheem Sterling tumbled in the area under a challenge by Marc Wilson.
Stoke boss Mark Hughes accused Sterling of conning referee Anthony Taylor, while the Liverpool midfielder also appeared to handle the ball in the build-up to the incident.
"I think is more of a case to answer for handball," said Gallagher. "I can understand why the referee has given the penalty. The defender has given him a decision to make.
"Sterling looked around after the handball; I think he expected a free-kick to be given against him. I think it's a clumsy tackle by Wilson and can understand why the referee gave that."