With his contract expiring at the end of the 2021-2022 campaign, Mbappe was heavily tipped to swap PSG for Madrid, which has made no secret of its admiration.
However, a transfer did not materialise as Ligue 1 giant PSG – still determined to re-sign the France international – refused to part with Mbappe.
Madrid is expected to sign Mbappe as a free agent at the end of the current campaign but the 22-year-old was asked about his frustration at the failed swich to the Santiago Bernabeu.
"Disappointed with not leaving? A little," Mbappe said.
"It's not easy, but whatever happened, I was going to play for a great club. I'm Parisian, I feel great, but I wanted to discover something else."
Speculation had mounted about Mbappe's future at Euro 2020, when the forward missed the decisive spot-kick in France's last-16 penalty shoot-out defeat to Switzerland.
Mbappe failed to score at the Euros and provided one assist as world champions France fell well short.
"During the Euros they asked me a lot of questions. I talked a lot with my parents, I knew I wanted to go out," Mbappe said. "My parents told me to concentrate on the pitch. Maybe I was putting too much energy into other things."
Mbappe, who joined PSG from French rivals Monaco initially on loan in 2017, has won three Ligue 1 titles with the capital club.
PSG top Ligue 1 this season, boasting an 11-point advantage over Rennes after 17 rounds.
Despite PSG's lead, Mbappe, Neymar and off-season signing Lionel Messi are yet to fully play a cohesive attacking brand of football.
"We are aware that the three of us must do more, we cannot hide, we assume it," Mbappe said.
"If I am the boss? It is difficult when you are in a team with Neymar and Messi, it would be audacious to say it, although it matters little."
Mbappe has been involved in 15 goals this season in Ligue 1 (seven goals, eight assists), with only Bayern Munich's Robert Lewandowski (17), Madrid forward Karim Benzema (19) and Liverpool star Mohamed Salah (22) doing better in the top five European league.
In the 1-1 draw against Lens, Mbappe was decisive in coming off the bench for the first time in the top flight since 5 December 2020 (goal against Montpellier).