The 20-year-old, who featured up front as the Blancos swept aside Osasuna in the Copa del Rey on Wednesday, thinks Carlo Ancelotti's side has a great future.
Angel Di Maria completed the 4-0 aggregate Copa del Rey victory, after Cristiano Ronaldo scored a freak opener which was punched into the net by goalkeeper Andres Fernandez as he made a terrible mess of a long-range free kick from the Portugal captain.
Jese, who started up front ahead of Karim Benzema for Carlo Ancelotti's men in the cup tie, was thrilled that the team avoided slipping up in the second leg and hopes they can continue with their improvement in 2013-14.
"It was a good game that ended with our goal of winning and I am very happy with the team's victory," the 20-year-old told reporters. "Osasuna had the advantage of playing the second leg at home, but we've been great in both games. I'm training well and want to help out wherever I can.
"I can see the team's getting better, we are having a great time. The team can give much more in the future. I'm sure we will play better games and we must do so."
The victories at the Santiago Bernabeu and Pamplona have seen los Blancos qualify for the quarterfinals of the Copa del Rey, where they will face Espanyol.