The former Blancos and Red Devils star has spoken of the unique appeal of Europe's elite competition
The 37-year-old was an unused substitute as his new club booked its passage through to the quarterfinals of the competition with a 3-2 aggregate victory over Valencia on Wednesday night.
The match represented Beckham's first involvement on club football's biggest stage since figuring for AC Milan against his boyhood club Manchester United during the midfielder's second loan spell with the Rossoneri in 2010.
"The MLS was an amazing experience, but I always missed the Champions League," Beckham told Canal Plus.
The former LA Galaxy star won two MLS Cups during the six years he spent in America, but for Beckham the Champions League always held a certain allure.
He added: "When you have tasted and won the Champions League, you cannot help but miss it.
"As soon as the music starts you feel something special. There are not many games which can produce this atmosphere."