Hospital-acquired infections (HAIs) are a global public health concern. As the COVID-19 pandemic continues, its contribution to mortality and antimicrobial resistance (AMR) grows, particularly in intensive care units (ICUs). A two-year retrospective study from April 2019–April 2021 was conducted in an adult ICU at the Hospital for Infectious and Tropical Diseases, Belgrade, Serbia to assess causative agents of HAIs and AMR rates, with the COVID-19 pandemic ensuing halfway through the study. Resistance rates >80% were observed for the majority of tested antimicrobials. In COVID-19 patients, Acinetobacter spp. was the dominant cause of HAIs and more frequently isolated than in non-COVID-19 patients. (67 vs. 18, p = 0.001). Also, resistance was higher for imipenem (56.8% vs. 24.5%, p < 0.001), meropenem (61.1% vs. 24.3%, p < 0.001) and ciprofloxacin (59.5% vs. 36.9%, p = 0.04). AMR rates were aggregated with findings from our previous study to identify resistance trends and establish empiric treatment recommendations. The increased presence of Acinetobacter spp. and a positive trend in Klebsiella spp. resistance to fluoroquinolones (R2 = 0.980, p = 0.01) and carbapenems (R2 = 0.963, p = 0.02) could have contributed to alarming resistance rates across bloodstream infections (BSIs), pneumonia (PN), and urinary tract infections (UTIs). Exceptions were vancomycin (16.0%) and linezolid (2.6%) in BSIs; tigecycline (14.3%) and colistin (0%) in PNs; and colistin (12.0%) and linezolid (0%) in UTIs. COVID-19 has changed the landscape of HAIs in our ICUs. Approval of new drugs and rigorous surveillance is urgently needed.