We aimed at evaluating the prognostic capacity of the inflammatory indices derived from routine complete blood cell counts in two groups of patients with acute pancreatitis from two different time periods, before and during the COVID-19 pandemic, when a high incidence of complications with surgical risk and mortality was found. Two new markers were introduced: the mean corpuscular volume to lymphocyte ratio (MCVL) and the cumulative inflammatory index (IIC), which were calculated at a baseline in the two groups of patients. Of the already established markers, none of them managed to effectively predict the complications with surgical risk and mortality, with a decrease of less than 50% in specificity in the peri-COVID group. The MCVL had the best prediction of complications with surgical risk in both the pre-COVID and peri-COVID groups, validated it as an independent factor by multivariate analysis. The IIC had the best prediction of mortality in both periods and was proven to be an independent factor by multivariate analysis. As the IIC predicted death best, we tested the occurrence of death and found that patients with PA who had an IIC > 12.12 presented a risk of death 4.08 times higher in the pre-COVID group and 3.33 times higher in the peri-COVID group. The new MCVL and IIC independent markers had a superior sensitivity and specificity in predicting surgical risk complications and, respectively, mortality in the group of patients with acute pancreatitis during the COVID-19 pandemic, which makes them widely applicable in populations with modified immune and inflammatory status. Conclusions: In patients with acute pancreatitis, MCVL has a significant predictive value regarding complications with surgical risk (abscess, necrosis, and pseudocyst), and the IIC has a significant predictive value for mortality.