Zinedine Zidane’s men are on a high after coming from behind to defeat Barcelona 2-1 in El Clasico on Saturday, despite the dismissal of Sergio Ramos.
It leaves Real still seven points off the pace in the Primera Divison, but Carvajal is looking to continue their recent good run of form, which includes six consecutive wins, with an attacking performance against Wolfsburg.
The 24-year-old said: “We’re going to win, not thinking about the second leg at our stadium.
“We have to go out as strong as possible for the first half hour, try to get on top of the opposition and to get goals. We know scoring away from home is very important so we’ll go for it.”
Los Blancos have been in fine form in Europe this season, conceding just three goals, and are currently unbeaten as they seek to claim an unprecedented 11th European title.
Carvajal acknowledged the importance of a defensive unit that is likely to be without Raphael Varane due to an ankle injury.
“It’s very important to not concede goals,” he said. “This is the key to the Champions League: if you don’t concede, you have half a foot in the next stage.”
He added: “The road would be to eliminate Wolfsburg and go on to win the 11th.
“At the moment we’re thinking about this tie, and it’s going to be difficult, it’s not just any team that makes it to the quarter-finals.”
Toni Kroos has warned Madrid not to believe Wolfsburg will be “pushovers” tonight.
“There are no pushovers in the quarter-finals,” Kroos said.
“If we go out thinking that, having won at Barca, we’ll beat Wolfsburg at half-speed, things are going to get tough. We have to give everything.”
Their opponents, Wolfsburg, have already created history having reached the last eight of the competition for the first time.
After beating Manchester United to qualify from Group B, the German side went on to beat Gent 4-2 on aggregate before being drawn against Real Madrid — a game which has added meaning for midfielder Josuha Guilavogui.
“This is a derby for me,” he said. “I was part of the Atletico squad that beat Real Madrid 1-0 with a goal from Diego Costa, so why not aim to repeat that kind of performance?
“Of course we will need to defend well because they have such a strong attack with Karim Benzema, Gareth Bale and Cristiano Ronaldo, so we will need to defend really well and then play well on the counter.”
Team-mate Marcel Shafer added: “When you think that 20 or 25 years ago you were watching Real Madrid on TV, and now you’ve got the chance to play against them, it is a fantastic challenge.
“We know we only have a very small chance, but we have nothing to lose.”