Carvajal, 28, joined Real Madrid the previous summer in a £5m move from Bundesliga side Bayer Leverkusen and quickly excelled despite the club's high expectations.
During this season, he was able to cement his standing as one of the world's best fullbacks as Carvajal displaced Alvaro Arbeloa - becoming Real Madrid's first-choice at right-back.
He started all but one of their Champions League knockout games that season and while making 45 appearances across all competitions in 2013-14, one match will be remembered in his mind forever.
Real Madrid were 1-0 down against city rivals Atletico after Diego Godin's first-half header and as the clock continued to tick down, were destined to suffer a narrow Final loss.
Sergio Ramos' bullet header in second-half stoppage time forced extra-time, where Atletico players were physically depleted and Real Madrid took full advantage, ultimately recording a 4-1 (AET) victory after goals from Gareth Bale, Marcelo and Cristiano Ronaldo.
The fullback tweeted in both English and Spanish for his supporters to understand, saying:" 6 years already of [since] that night when everything changed", accompanied by some trophy emojis. You can view Carvajal's tweet here, with fans responding as they reflect with him:
One fan said Carvajal's presence was an under-rated part of Real Madrid's Champions League success that season. They crashed out at the semi-final stage in each of the previous three years before his arrival in their first-team.
Carvajal reminisces, as Real Madrid will return in June
Carvajal's latest tweet comes a day after Spain prime minister Pedro Sanchez confirmed that La Liga will be free to resume from June 8.
During a speech, he was quoted as saying: "The time has come to resume many daily activities. From June 8, La Liga will return - Spanish football has a huge following."
Spain's top-flight is still expected to resume their 2019-20 season on Friday June 12, as opposed to the start of a working week.
They will be the second top European league to resume after Germany's Bundesliga, and Barcelona hold a two-point gap to closest rivals Real Madrid in a slow-burning title race.
With 11 La Liga matches still to play, Zinedine Zidane's side will be quietly confident they can dethrone Barca - even after the coronavirus pandemic delayed an inconsistent season for Spain's top two sides.
Carvajal made 30 appearances across all competitions before March's suspension, including their 2-1 last-16 first leg home defeat by Manchester City in the Champions League.
On Saturday May 22, Spain recorded 466 new COVID-19 cases and a further 50 deaths - taking the death toll up to 28,678 across the nation.