The on-loan Paris Saint-Germain forward reportedly walked down the bet365 Stadium tunnel and left the ground after manager Mark Hughes made his second and third substitutions in the 70th minute.
Hughes confirmed that Jese understood that his actions were not "the right decision at that time" and that they were dealt with accordingly by the club.
Speaking ahead of Stoke's weekend Premier League meeting with Tottenham Hotspur, the Welshman told reporters: "He made a mistake. He's been disciplined for that.
"He understands it wasn't the right decision at that time. It's been addressed, we've obviously highlighted what he needs to do in the future. He's a little bit frustrated, he wants to play, as all players do."
Asked if Jese had apologised, Hughes added: "Not in so many words because his English isn't great but he understands that it was incorrect."
Jese lost his place in the side after the 2-1 defeat against Bournemouth in October and has made just two substitute appearances since.