You'd think that tiki-taka relies on unattainable levels of coordination and high training between players, but it's not that simple. Barcelona's believed in a high-possession, fluid mentality since Johan Cruyff, but their tactic and style under Frank Rijkaard was far more flashy and flair-driven than Guardiola's patient, possession-driving short-passing game.
It also turns out that a high-possession short passing style is within the grasp of many teams. Look at Swansea in the Premier League this past season.
And it oversimplifies things to say that England is all kick-and-rush and continental Europe is more focused on possession. For one, some English clubs have favored possession for decades, including Arsene Wenger's Arsenal. For another, counterattacking, as opposed to patient, possession-driven build up play, is very popular in Italy. If you saw much of Italy before the final, they did appear to "hoof it up to the big striker"--but really, they were making pinpoint passes down the length of the field right as Balotelli broke the onside trap. And the teams that do beat Barcelona, continental and otherwise, seem to do so by abandoning possession and "parking the bus"--Jose Mourinho's Inter would even clear the ball as soon as they managed to win it as to hold their defensive shape, rather than try to make attacking moves and be drawn out of position so they were vulnerable to Barcelona's attack.