The Cold War had little to no effect on the competitions themselves, but the political/economic structure of the Warsaw Bloc directly affected the way football clubs in Eastern Europe were set up. For example, while football clubs in Western Europe pursued various ownership models (fan/member ownership, the public company model, private ownership, etc), clubs in Eastern Europe were almost all owned by a certain institution either owned by or directly being a part of the state. For example, many of the Eastern European football clubs were owned by the respective country's external defence/military branch (Partizan in Yugoslavia, CSKA Moscow in the USSR, etc). Help from the state allowed many Warsaw Bloc teams to prosper despite the lack of funds available.

As far as the competitions went, there weren't any particular animosities between the teams themselves. UEFA adhered to a strict political neutrality policy that's still in effect today. Western/Eastern teams treated each other just like how two teams from different Western European nations would treat each other nowadays. The only big difference between modern football and Cold War era football in this regard is that there were little to no away fans if the fixture presumed crossing the Iron Curtain.