Centaurus A, the cosmic ray accelerator a few Mpc away from us, is possibly one of the nearest sources of extremely high energy cosmic rays. We investigate whether the gamma ray data currently available from Centaurus A in the GeV-TeV energy band can be explained with only proton-proton interactions. We show that for a single power law proton spectrum, mechanisms of γ-ray production other than proton-proton interactions are needed inside this radio-galaxy to explain the gamma ray flux observed by EGRET, upper limits from HESS/CANGAROO-III and the correlated extremely energetic cosmic ray events observed by the Pierre Auger experiment. In future, with better γ-ray data, and simultaneous observation with γ-ray and cosmic ray detectors, it will be possible to carry out such studies on different sources in more detail.