Modric received 313 points in the vote, which included 60 coaches and 55 journalists from across Europe, to beat Ronaldo by 90 points with Liverpool's Mo Salah finishing a distant third.
But super-agent Mendes was furious that Ronaldo, who signed for Juventus earlier in a club-record deal last month, did not beat out Modric for best player honours.
The Portugal captain scored 15 goals in 12 games and finished as the competition's top scorer as Real romped to a third consecutive Champions League title.
"Football is played on the field and that's where Cristiano won," he told Portuguese outlet Record.
"He scored 15 goals, carried Real Madrid on his back and conquered the Champions League again.
"It's ridiculous, shameful. The winner is not in doubt, as Ronaldo is the best in his position."