Madrid lost the La Liga title by a single point last season, and Carvajal is sure they will not leave any stone unturned this season.
Madrid and Barcelona were potential winners of the title last season, but Barcelona secured a win that won them the title.
Carvajal is desperate for Madrid to drop as few points as possible, having missed out by such a small margin last term.
“It’s a nice record to equal the 16 victories, but we must keep thinking game by game,” said the right-back.
“Now we are thinking about three points on Wednesday against Villarreal, but what we are seeing is a reflection of the great work from Zidane and the team.
“La Liga has just started, we are going into matchday five and there are 38 [matchdays]. We think about adding three [points] because last year at the end we lost by one point.
“All are important and we are not going to give any away.”
Zidane took over at the Santiago Bernabeu in January and, under his stewardship, Madrid have dropped just seven points in the Spanish top division.
The 1998 World Cup winner’s man-management has been key to the club’s stellar run, according to Carvajal.
“He has found the key to making everyone feel important,” he added. “And keeping the egos apart – that is the basis for success today and I hope it remains so.”