First of all, it's important to note that the percentage of cars (worldwide) that uses a manual gearbox was 43% in 2015 and is expected to drop to 36% in 2025. Already the automatic transmission and continuously variable transmission (combined) are the most popular gearbox type, not manual transmission.

As for its popularity in the USA vs. Europe, American automobile manufacturers were at the forefront of automatic gearbox development just prior to the outbreak of the Second World War; especially General Motors with its so-called Hydra-Matic gearbox. After the wars conclusion (which left the USA as one of the few participants with little to no damage to its industry and/or financial reserves) the American economy soon flourished and demand for new cars (which had been scarce during the war years) was high. General Motors did not keep its gearbox to itself and instead sold the patent to most other American brands. Its availability became such that, with increased consumer spending power, it ceased to be a luxury and instead became a standard option on most American cars. They soon became so ubiquitous, that an automatic gearbox became the standard; rather than the exception. Later, when foreign brands tried to access the American market; they adapted and tended to make their models automatic as well.

In wartorn Europe, cars in general (let alone luxury cars) were not an option for the average consumer. European car manufactures hence tended to focus on affordable, simpler cars based on tested and proven technology (for example the VW Beetle and Citroën 2CV) for a less affluent market. In Europe automatic gearboxes never became the standard, as in the USA. They remained a luxury option for most car makers for a long time, with automatic gearboxes remaining more expensive than their manual transmission equivalents to this day.

This does not however, mean that there are no automatic gearboxes driving around in Europe. Indeed, most of the more luxurious models of European brands tend to have an automatic gearbox rather than a shift gearbox. They just never took over the market in the same way that automatic transmission did in the USA during the fifties.