The Citizens took the lead in the 22nd minute, but the hosts got the equalizer through Jetro Willems three minutes later.
Kevin De Bruyne scored what looked like the winner in the 82nd minute before Jonjo Shelvey latched on to Christian Atsu’s pass to hand a blow to City’s title challenge.
Pep Guardiola’s men are now eleven-points behind runaway league leaders Liverpool after their stalemate against the Magpies.
Stones admitted that the result is hard to take but insists the title challenge will go down to the wire.
"That result is hard to take. The dressing room is really flat,” the former Everton defender told reporters.
“Everything happened so quickly in the last ten minutes from elation to deflation. It’s a difficult one to take.”
He added: "They set up defensively right from the off. We conceded two sloppy goals today and that has cost us today.”
“The chase is still on. We fight until the last day. That’s what we did last season. Anything can happen. Today we played some unbelievable play but those mistakes cost us."
Manchester City manager Guardiola also insisted that he is not happy with the result but his team really played well today.
"We played at a good level. It was not easy because they defended deep. We scored two goals but we also let two in which is disappointing.
"With substitutions sometimes players forget positions. We found a way to get through but we unfortunately at the end we conceded a goal.”
“There are teams that defend deeper like this, it happens all season. We do the same work we have done over the last few seasons. We tried to score more goals but it did not happen."
