France international Griezmann netted six goals along with two assists to scoop the best player prize and the Golden Boot, but his side were beaten by Portugal in the final of the competition.
Pepe was central to that triumph, and Ronaldo – who featured alongside him in the Team of the Tournament – claims the 33-year-old defender would have been a worthier winner.
“In my book, Pepe was extraordinary this year,” he told UEFA.com. “It was possibly his best season.
“He was undoubtedly Portugal’s best player and one of Real Madrid’s best players in the Champions League.
“I’m delighted he was selected in the Team of the Tournament at the Euros – in my opinion Pepe was the best player at the Euros.”
Ronaldo is on a three-man shortlist for UEFA’s Best Player in Europe award, along with Madrid colleague Gareth Bale and Griezmann, with the winner due to be announced on Thursday.