Rudiger scored his first goal for Chelsea on Wednesday night as Antonio Conte's men saw off Everton 2-1 in their Carabao Cup fourth-round win at Stamford Bridge.
The Blues will now play Bournemouth at home in the quarter-finals, and Rudiger admits the competition is one that Chelsea - who failed to add the FA Cup title to their Premier League crown last term - should be aiming to win.
He told Chelsea's official website: "You can win a trophy, so you have to be motivated. It was a big chance as well for young players like Ampadu, Musonda and Kenedy.
"Everyone has to be motivated and for our club this is the fastest way to win something, so we have to go for it."
Rudiger's first goal for Chelsea came after Charly Musonda crossed the ball in from the left for the defender to head past Jordan Pickford in the 26th minute.
And he later admitted that luck played a role in his debut goal, though he was pleased to simply get off the mark at Chelsea following his move from Roma in the summer.
"I am very, very happy we won the match and I could contribute to the result," he added.
"I am very happy to score my first goal for Chelsea. The thing is, I didn’t see the ball because of the light. I was looking up. It was a good header but a bit of luck also as well."