If you look at lists of the most popular cars built by European manufactures, and cars sold in European countries, they are dominated by smaller cars.
In post WWII Europe the cars that sold in greatest numbers were the VW Beetle, Fiat 500, Citroen 2CV, Renault 4, and the Austin Mini. With the exception of the Beetle these cars all had engines less than 1 litre in size (63 cubic inches) and none of these cars had engines producing more than 50bhp (although some later variants did). The low weight and power of these popular vehicles were unsuited to the complexity, weight, and expense of torque converter automatics favoured by larger and more powerful US cars. It's worth noting that the Citroen 2CV and Fiat 500 were available with centrifugal clutches which give an automatic like experience when stopping or moving off, but require a clutch pedal to change gears.
European taxation also encourages the sale of smaller, less powerful, and more economical engines. so manual gearboxes dominated European cars sales. Europeans grew up with manual gearboxes being the default choice for the vast majority of cars. If you couldn't drive using a clutch you were limited to larger, more expensive, and rarer cars.
It's only the last few years as dual clutch gearboxes, forced induction engines, and engine management systems have become more advanced that the penalty for automatic gearboxes has been reduced and they can be run as economically as manual cars. In fact, the level of electronic integration between engine and gearbox is now close that modern automatic gearboxes can be driven more economically than manuals, so the last few years has an increase in the percentage of automatics sold in Europe.
Short answer: The technology behind modern automatic transmissions was first developed by General Motors and Chrysler during the 1930s, and the first automatic cars were offered by those manufacturers, beginning with a manually shifted but clutchless GM transmission in the late 30s. Fully automatic GM products debuted in 1940, and Chrysler products of the 1940s also featured semi-automatic fluid coupling transmissions.
European manufacturers didn't develop their own automatic transmissions until much later (1961 in the case of Mercedes-Benz). By that point, the postwar consumer preferences on both sides of the Atlantic had already been established.
Longer answer: The early European car market featured a wide array of makes and models, with each country host to several manufacturers. While engine, suspension, and body choices varied widely, nearly all employed the Panhard-style design we now call a "manual transmission."
In contrast, the early American car market was dominated by exactly one car: the Ford Model T. By 1919, the Model T accounted more than half of all cars sold each year in the United States. The T became a de facto standard in America; the Sears catalog featured all kinds of accessories to turn T's into everything from a washing machine to a snowmobile.
The Model T featured a planetary transmission with no clutch pedal. While the driver still had to choose between low, high, and neutral using a foot pedal, both the technical workings of the transmission and the overall driving experience were more like an automatic transmission than the pre-synchro manual transmissions of the time.
Because of the Model T's absolute dominance of the early US car market (and subsequent presence on the used car market as late as the 1950s), entire generations of Americans learned how to drive (and repair) a car with no clutch pedal.
A fun quote from John Steinbeck: “Someone should write an erudite essay on the moral, physical, and esthetic effect of the Model T Ford on the American nation. Two generations of Americans knew more about the Ford coil than the clitoris, about the planetary system of gears than the solar system of stars[emphasis mine]. With the Model T, part of the concept of private property disappeared. Pliers ceased to be privately owned and a tire pump belonged to the last man who had picked it up. Most of the babies of the period were conceived in Model T Fords and not a few were born in them. The theory of the Anglo Saxon home became so warped that it never quite recovered.”
Because of the Great Depression and WWII, many Americans continued operating clutchless Model T's until the late 30s or even the 40s, by which point automatic transmissions were available. At the very least, clutchless driving would have been familiar and comfortable to an American driver of the 1940s.
EDIT, TLDR: The reasons behind this are more historical than technical.
Perhaps a better question for /r/AskEngineers?
There have been many long answers posted, but I will repeat one of them, paraphrase another and attempt to keep it short:
As a result, most of these vehicles were very low performance and the addition of an automatic transmission would have reduced performance into an unusable range - even by European standards.
Case in point: the VW Bug didn't really take off in popularity (in the US) until the '60s. My wife owned a 1962 bug. It had a 36 horsepower engine. Driving it was always fun as you kept the pedal to the floor at all times and you took any curve as fast as you could so as to scuff off as little speed as possible. Other european cars such as the Citröen 2CV or the Fiat 500 were so low-powered as to be unsuitable for American roads.
An automatic-transmissioned car gets significantly lower m.p.g than a manual transmissioned vehicle.
For the above-mentioned balance-of-payments reason, European countries taxed gasoline heavily, and it was/is sold per litre rather than by gallon so as to discourage consumption.
Today, while we complain about $4/gallon gas, it is (the equivalent of) $8-9/gallon in Europe.
When I was dating, gasoline cost twenty-five cents per gallon and the automatic-transmissioned car I drove got six to ten m.p.g. Fuel mileage? Who cares!