The club have waved goodbye to 12 members of their squad this summer, including top scorer Piti, who joined Granada, fans' player of the year Alejandro Dominguez, who left for Olympiacos, and Leo Baptistao, who signed for Atletico Madrid for around 7million euros (£6 million).
Meanwhile, nine new players have been recruited, among them Atletico Madrid youngster Saul Niguez (on loan), former Valladolid midfielder Alberto Bueno and Mexico international Nery Castillo.
Despite the squad revamp, Jemez is confident his team will be successful in the La Liga, as long as they follow the same steps they took last year.
He told a press conference: "We want to continue with the same dynamic. It's vital that we play with intensity, enthusiasm and with ambition because that needs to be our starting point if we are to be different from the rest of the league.
"I'm very happy, because that's the direction we need to move in, and I know that everyone's going to compete at a high level.
"The new arrivals have adapted to that dynamic very quickly and our long standing players have played a big role in making sure everyone fits in."
The Madrid club open their league campaign at home to Elche, and Jemez is aware that the newly-promoted side will be keen to make an impact on their return to the top flight.
"Elche have just been promoted, they have gone a very long time without being in the Primera Division and they have built a strong squad," he said.
"They have made some important signings and they are going to come here to make things difficult for us. It's not going to be easy, they are a hard working and organised team who leave few spaces, and we will have to be patient and keep our cool if we want to cause them damage."
Elche boss Fran Escriba declared his team were confident in their ability and were determined to return from Vallecas with all three points.
"We are convinced that we can achieve our objective and win the game," he told reporters.
"None of us will be happy with a draw. We know that this is the top-flight but our squad is good enough to compete with any team."
Damian Suarez and Ruben Perez are suspended for Elche, while Rayo forward Jose Carlos is out with an ankle injury.