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The French striker missed a penalty in Real Madrid's 2-0 defeat to Liverpool at Anfield.
After four consecutive Clasico defeats, Barcelona claimed their first triumph over Real since March 2023.
England midfielder Bellingham was phenomenal for Real last season, when they did not have Mbappe, scoring 23 goals with 13 assists in 42 appearances in all competitions.
France coach Didier Deschamps left Mbappe out of the squad he announced on Thursday, saying the 25-year-old lacked preparation, having played too few matches.
Jonathan David converted from the spot three minutes into first-half stoppage time to hand Real, who had not lost in their previous 36 matches in all competitions, their first defeat since January.
Mbappe, signed from Paris St Germain this year, has been in fine form this season, scoring seven goals for Real in nine matches across all competitions.
Every team will play eight games against different opponents in the new format of Europe's elite club competition.
Mbappe rifled home in the 68th minute after Jude Bellingham spotted his dart into space in the box to seal the victory.
The France striker, who had completed his medical earlier on Tuesday morning, signed a five-year contract and was handed a No. 9 shirt by club president Florentino Perez.
The 34-year-old Spain international has won six Champions League titles with Madrid since joining their youth academy in 2001, as well as four LaLiga crowns, two Copa del Reys.
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