Ronaldo failed to score in his opening two games but responded to heavy criticism by netting a brace in Portugal's 3-3 stalemate with Hungary in Lyon.
The draw helped Portugal finish third in Group F, setting up a last-16 meeting with Croatia after qualifying as one of the best third-placed teams.
"It's always very important to have a good captain, especially a captain who is also worth a lot of goals," he told A Bola.
"We hope these are the first of many."
Ronaldo became the first player to score in four European Championships with his goals against Hungary.
Portugal lock horns with Croatia, who pipped defending champions Spain to top spot in Group D, in Lens on 25 June.