The Gunners took a 3-0 lead to the Bernabeu and left with a 5-1 aggregate win after goals from Bukayo Saka and Gabriel Martinelli secured victory in both games.
It was a hugely impressive display across both legs from Mikel Arteta's side, but equally disappointing from the reigning champions Madrid, who barely laid a glove on their opponents.
And Courtois - who saved a Saka penalty in the first half and pulled off a number of other excellent saves across the two games - claimed his side need to play more as a team.
"We are a team, but sometimes I feel like we play too individually," he told CBS Sports after the game.
"When they double-team Vini or Kylian (Mbappe), sometimes it works out, but three, four times, it doesn't. If we want to win, we need to be better."
Vinicius did get on the scoresheet, pouncing on a William Saliba error to give his side false hope, but there was no such joy for Mbappe.
And Courtois aimed a thinly-veiled jibe at the Frenchman by claiming they missed not having a "natural striker", name-checking Joselu.
"In the end, they're a team that defends well, is well organised, presses well, and it's difficult to find space," Courtois said as he gave credit to Arsenal.
"We put in a lot of crosses, but this year we don't have Joselu, a natural striker up front."
Joselu came off the bench to score twice in Madrid's dramatic semi-final win over Bayern in the Champions League last season but was sold to Qatari side Al-Gharafa in pre-season when Mbappe arrived on a free transfer from PSG.
Mbappe has scored 32 goals in his maiden season in Spain, including seven in the Champions League, but he was kept quiet across both legs against Arsenal.
Carlo Ancelotti's side are still chasing two trophies, with Carlo Ancelotti's men four points behind Barcelona in La Liga, while they will also face their arch-rivals in the Copa del Rey final later this month.
They will also compete in the all-new Club World Cup at the end of the season and Courtois urged his teammates to bounce back quickly with plenty left on the line this season.
Real Madrid have reportedly struck a strategic deal with Arsenal, securing priority access to star defender William Saliba should the Gunners ever decide to sell him before his contract expires in 2027.
Bayer Leverkusen head coach Xabi Alonso has chosen not to comment on growing speculation linking him with a potential return to Real Madrid for next season, insisting that now is not the appropriate time to discuss his future.
Arsenal manager Mikel Arteta has expressed confidence that forward Kai Havertz could make a surprise return from injury before the end of the season, raising hopes that the German international may be available for their UEFA Champions League push.
Arsenal have reportedly cooled their pursuit of Wolverhampton Wanderers' forward Matheus Cunha due to concerns over his on-pitch behaviour, according to recent reports.
