The use of air-source heat pumps (ASHP) is increasing to meet the energy needs of residential buildings, and manufacturers of equipment have permanently expanded the range of work and improved the coefficient of performance (COP) in very adverse outdoor air conditions. However, in the time of a wide range of different technologies, the problem of using ASHP, from a techno-economic point of view, is constantly present. Although exergy is the only thermodynamic parameter compatible with economic principles, methods based on conventional exergy analysis are no longer able to respond to the extremely demanding needs of the actual market. Exergetic efficiency and exergoeconomic cost no longer provide sufficiently reliable information when it is necessary to reduce the investment costs or increase the energy/exergetic efficiency of the component/system. This paper presents a performance comparison of ASHP in different real operational conditions based on an advanced exergy and exergoeconomic approach. The advanced exergy analysis splits the destruction of exergy for each individual component of the heat pump into avoidable and unavoidable exergy destruction in order to fully understand the processes. In exergoeconomic performance evaluation, the information of stream costs is used as the information to calculate exergoeconomic variables associated with each system component. Irreversibilities in the compressor have the greatest impact on reducing the overall system exergetic efficiency by 46.7% during underfloor heating (UFH) operation and 24.53% during domestic hot water (DHW) operation. Exergy loss reduces exergetic efficiency by 5.72% (UFH) and 39.74% (DHW). High values of exergoeconomic cost for both operating regimes are present in flows 1, 2, 3 and 4 due to high costs of production and relatively small exergy levels. The general recommendation is to set the ASHP to operate with near-optimal capacities in both regimes and then reduce exergy of flows 1, 2, 5, 11 and 13. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 451-03-68/2020-14200109]