On Sunday, the 25-year-old said he believed Williams had contravened the players' usual protocol. "I wasn't angry or frustrated. Maybe for a couple of minutes or so. It is just the principle," he said.
With Bopanna's tame defeat, India's challenge has ended at the €6,408,230 clay tournament.
Indo-Uruguay pair lost 6-7 (3) 6-7 (2) to the combination of Henri Kontinen and John Peers.
Bopanna and Cuevas won 6-3, 3-6, 10-4 in one hour and 14 minutes at the Monte Carlo Masters.
The Indo-Uruguayan pair will now contest Poland's Romain Arneodo and France's Hugo Nys.
They next face top seeded team of Henri Kontinen from Finland and Australia's John Peers.
Bopanna and Cuevas overcame a strong challenge to win the first round clash 6-3, 6-7, 10-2.
Bopanna and Cuevas lost 6-2 3-6 10-7 to the Serbian combination in one hour and six minutes.
Cuevas won 2008 French Open with Luis Horna and has five ATP singles titles to his credit in eight finals.
