Burst suppression (BS) activity in electroencephalogram (EEG) is clinically accepted as a marker of brain dysfunction or injury. Experimental studies in a rodent model of brain injury following asphyxial cardiac arrest show evidence of BS soon after resuscitation, appearing as a transitional recovery pattern between isoelectricity and continuous EEG. The EEG trends in such experiments suggest varying levels of uncertainty or randomness in the signals. To quantify the EEG data, Shannon entropy and Tsallis entropy are examined. More specifically, an entropy-based measure named Tsallis Entropy Area (TsEnA) is proposed to reveal the presence and the extent of development of BS following brain injury. The methodology of TsEnA and the selection of its parameter are elucidated in detail. To test the validity of this measure, 15 rats were subjected to 7 or 9 min of asphyxial cardiac arrest. EEG recordings immediately after resuscitation from cardiac arrest were investigated and characterized by TsEnA. The results show that TsEnA correlates well with the outcome assessed by evaluating the rodents after the experiments using a well established neurological deficit score (Pearson correlation = 0.86, p << 0.01). This research shows that TsEnA reliably quantifies the complex dynamics in BS EEG and may be useful as an experimental or clinical tool for objective estimation of the gravity of brain damage after cardiac arrest.