Benitez will take charge of his first competitive game when Real travel to Sporting Gijon to get their La Liga campaign underway on Sunday.
Despite spending hundreds of millions of euros, Madrid have managed to win just one league title in the past seven seasons.
However, Benitez shrugged off suggestions that La Liga must be the priority over the Champions League this season because as a former player and youth coach at the club he knows the expectation is to win everything.
"I know what the people think, the fans and our members think, they want the team to win the league but also the Champions League and the Cup," said Benitez.
"To win the league we have to start well against Sporting.
"But when the Champions League and Cup games arrive the demands will be the same.
"It is not a surprise that we have to win titles. It is normal at Real Madrid.
"We will do it by working hard and taking advantage of the individual talent that we have," added the 55-year-old.
Benitez has also insisted that his side maintain a balance between attack and defence.
However, his squad appears overloaded with midfield players, whilst Karim Benzema remains the only out-and-out striker on the club's books.
Benitez denied reports he was looking for another striker to arrive at the Bernabeu before the transfer window closes and reaffirmed that Arsenal-target Benzema will be central to his plans this season.
"I am convinced that Benzema is a fantastic striker, that is why I have given him the target of 25 goals.
"We have (Cristiano) Ronaldo, Jese and Borja Mayoral who have been extra options in pre-season. Therefore, at the moment we are not looking for another striker."
One of the motives behind not bringing in another striker appears to be Gareth Bale's desire to play through the middle this season.
Benitez, though, insisted that all his forward players will have freedom to move so there won't be a drastic change to Bale's positioning compared to his first two seasons in Madrid.
"The position of Bale is like Isco, Jese, James (Rodriguez), Cristiano. They are offensive players with talent and liberty to move in the pitch where they will be most effective.
"Bale has pace, a great shot, physical power and the others have different characteristics.
"Those different qualities allow us to be more unpredictable and harder to stop."
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