Benzema becomes the fifth madridista in standings for European Cup games
Shakhtar game was the Frenchman's 102nd in the competition, in which he has scored 53 goals.
Modrić and Vinicius Jr. scored in the second-half for the madridistas, who came close to coming back from three first-half Shakhtar Donestsk goals.
"There are difficult moments in football as we have seen in the past and we have to lift our heads up and stick together", said the coach.
Florentino Pérez presented Palkin Sergei with a replica of the Cibeles and a commemorative jersey of the match.
The French magazine will reveal the names of the 11 members of the dream team in December.
Following the first year of redevelopment work, the transformation of the madridistas' stadium is now apparent.
It will be held on November 4 in person but is already available online with the benefits going to Real Madrid Foundation projects.
Real Madrid are celebrating the anniversaries of the club's 13 European Cup triumphs during the period between 11 May and 13 June.