The Chelsea goalkeeper notes his teammate's reaction to seemingly being bitten on the arm by the Liverpool forward, who later went on to net an injury-time equalizer.
The Czech Republic international feels that, though he did not see the particular altercation, the Uruguayan had been pushing his luck with small offenses throughout the game.
"I didn't see it at the time but people have told me which is surprising," Cech told BBC Sport. "Suarez always does little fouls and pushes. I saw Branislav's reaction and he was not happy at all.
"Every time Luis Suarez is close, he pushes defenders around. I was complaining to the referee about it."
However, Liverpool captain Steven Gerrard defended the Uruguayan's actions in the second half, in which he also gave away a penalty for a handball, which Eden Hazard scored.
"I think it would be an injustice to Luis Suarez to talk about 45 minutes. He has been the best player in the league this season," the Reds midfielder insisted. "I think he is the third best player in the world behind Lionel Messi and Cristiano Ronaldo.
"You have two good teams, there is a lot at stake. These games will get spicy."