The 21-year-old injured his cruciate knee ligaments in Real Madrid's 3-1 win over Schalke on Tuesday, putting a dampener on their progression to the quarter-finals.
Jese has developed as a serious prospect this campaign and had been mentioned as a possible dark horse for Spain's World Cup squad.
That will go on ice now, though, and Ancelotti is sad for a player he rates highly.
"I think it has been confirmed that Jese has torn his cruciate ligament. He was unlucky. I think that the whole of Real Madrid has been unlucky. We are going to lose a very important player, a young man who has done very well this season and surprised everyone," he told Madrid's official website.
"That is football. Injuries come in a player's career and we will be close to him and support him and we'll be waiting for him next season.
"We hope to have him ready soon and we would like to send him our support. We are waiting for him and we wish him luck. He will certainly be an important player for Real Madrid after his injury. We are sad. We are very sorry about this, but these things happen in football."
Ancelotti added that the other members of his squad were despondent about the injury, saying: "The squad is a bit down about it. It is normal when that happens to a player, like when it happened to (defender Sami) Khedira.
"It is another problem for everyone and we will respond well because the team has character."
Jese, meanwhile, is grateful for the encouragement he has received from well-wishers since suffering the injury.
He wrote on his Twitter account: "Heartfelt thanks to all of you, thanks for all the messages of support...!"