The incident occurred in the second half of the teams' 2-2 draw at Anfield when the Uruguayan lunged at the Serbian and appeared to bite him following an altercation in the penalty area.
"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."