Potato yield is affected by an interaction between nitrogen (N) and potassium (K) supply. This hypothesis was verified in a series of field experiments conducted during 2010–2013 in Albania (AL), Czech Republic (CZ) and Poland (PL). The two-factorial experiment was founded on relative scales of K (0, 50, 100, and 150%), and N application rates (75% and 100%) of the recommended doses, which were country-specific. The average tuber yield was doubled for AL, increased by 50% for PL, and by 15% for the CZ in response to K and N interaction. These differences are caused by an increase in the apparent nitrogen efficiency (ANE), which rose significantly by the progressive Krates. Maximum average ANE of 90 kg tubers/kg N was recorded in AL; it was 2-fold lower in CZ. Top average apparent potassium efficiency (AKE) of 65 kg tubers/kg K was recorded in PL; it was 4-times lower in CZ. The relationships between AKE and ANE clearly demonstrate the tight interaction between the N and K, and its effects on potato yield. However, a sound K application management should be adjusted to the local edaphic and climatic conditions.