Spain remain the reigning European champions despite surrendering their world crown in a meek fashion this summer, yet they will still need to prove they deserve to participate at the 2016 continental finals in France.
First up are Bosko Gjurovski's Macedonia in Valencia and, following last week's friendly defeat by France, Carvajal knows La Roja have to start brightly if they are to avoid further disappointment.
The Real Madrid right-back, who made his senior debut at the Stade de France, told sefutbol: "They'll be closed up at the back so we need to get out there and try to score soon so we can take control of the game."
Referring to the 1-0 loss in Paris, Carvajal added: "We created chances.
"It was a good game and we still felt that way even when we were leaving (France)."
Spain must cope without the services of prolific Chelsea striker Diego Costa against Macedonia after the Brazil-born hitman injured his hamstring against the French.
"He plays with his back to you and enriches the side," Carvajal added. "Any team would like to have him.
"He probably does not like being sidelined, but he will recover soon."
Macedonia have never qualified for a major tournament but may fancy their chances of grabbing third place and a shot at the play-offs.
Despite the retirements of defender Nikolce Noveski and forward Goran Pandev, head coach Gjurovski is optimistic his team can outperform at least one rival from Ukraine, Slovakia, Belarus and Luxembourg.
Midfielders Arijan Ademi and Ostoja Stjepanovikj are unavailable at the Estadi Ciutat de Valencia due to injury while winger Ivan Trickovski is struggling for fitness.
Ukraine kick off their qualifying campaign against Slovakia in Kiev and will hope political unrest in the country does not derail their bid to reach Euro 2016.
Slovakia's last experience of a summer tournament was a trip to South Africa in 2010. On that occasion, the eastern European nation outperformed then world champions Italy to reach the last 16 of the World Cup.
Minnows Luxembourg are also in action on Monday night. Coach Mario Mutsch is charged with delivering the duchy's first competitive victory since September 2013, but Belarus will provide stern opposition.
Georgi Kondratiev's men warmed up for their trip to the Stade Josy Barthel with a 6-1 friendly win against Tajikistan.