The midfielder stole in after a defensive lapse from the home side late on to hand City all three points, and Stones was pleased to see our persistence rewarded.
Reflecting on the result, the defender insists he and the players consider anything less than victory as a disappointment, regardless of the competition or opponent.
He said: "We have to win every game from now on, in every competition, we set ourselves that standard.
"We are not happy with ourselves to say the least when it doesn’t come off, but from now on we have to try and focus on every game.”
Stones also gave credit to Everton for their contribution to an enthralling Premier League contest.
"I thought it was a great game for the neutral, the atmosphere from both sides was incredible,” he reflected.
"It was a passionate game, and it went to the wire and just really glad to come out on top.
"There are fine margins in these games sometimes, I’ve got to give a lot of credit to them.
"They put us under a load of pressure, caused us a lot of problems that we had to deal with.”