The 24-year-old forward, who helped Real Madrid win the Champions League and La Liga, beat nine other nominees to the trophy.
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He took to social media after finishing second in the prestigious award voting behind Spain and Manchester City midfielder Rodriguez.
This was made possible by goals from Vinicius Jr and Arda Guler as well as own goals from Carlos Dominguez and keeper Vicente Guaita.
Los Blancos entered Tuesday’s quarter-final second leg with a strong advantage, having recorded a 2-0 win when the two teams locked horns at Bernabeu in the reverse fixture last week.
Real are second on six points behind Sheriff, who lost 3-1 at Inter Milan, taking the Italians to four points.
The 20-year-old Brazilian fired the 13-times European champions into the lead in the 27th minute at the Alfredo di Stefano stadium after controlling a long diagonal pass from Toni Kroos from his own half which flummoxed the Liverpool defence.
Brazilian forward Vinicius, Real Madrid’s match-winner in Wednesday’s 1-0 win over Real Valladolid, also gave his side the lead at Levante.
The hosts’ win has come after a week in which their pride had taken a beating at home and in Europe
Both sides seemed to be holding each other at arms’ length for much of the first half, but Jesus tested Thibaut Courtois after being slipped in by De Bruyne’s incisive pass, before City suffered a major blow as Aymeric Laporte limped off injured
Still reeling from their painful UEFA Champions League elimination by Ajax Amsterdam, Real Madrid said on Wednesday that Brazilian forward Vinicius Jr had suffered ligament damage in his right shin.