TLDR: Currently and historically, American manufacturers are very good at making big power from big engines to make big cars go big fast in a straight line. When the market needs suddenly shifted in the ‘70s, American reliability and power output dropped drastically, and Japanese automakers were already there with efficient and reliable cars to fill the gap. They maintained that reputation through today, while American reliability was extremely poor for a few decades, and has stayed spotty for a long time. The European cars imported to the States have generally had a focus on luxury and innovation, leading to more expensive and less reliable vehicles as well.
Long answer:
Toyota was the first Japanese automaker to sell cars in the US in 1958 and has pretty much always had a focus on ~~over engineering~~ manufacturing their vehicles in such a way as to be exceptionally reliable. They weren’t super popular, but became known for being reliable and easy to fix and maintain. (@MargotRobbie and @LordOfTheChia both go into better detail on this engineering philosophy beneath this comment)
In 1973 OPEC put an oil embargo on the United States and other countries that supported Israel. This drove oil prices through the roof and the market shifted from wanting big, flashy, and powerful “American muscle,” to needing cars that could do better than 4 miles per gallon. In addition, the US government started requiring more and more emissions and efficiency controls on cars being sold.
American manufacturers struggled to adapt their existing platforms to be more efficient while Japanese companies like Toyota and Honda had already been building simple and efficient cars for years. When the Japanese economy started booming and more of their manufacturing was moved to the States, the cost to purchase and maintain a Japanese car decreased further and led them to be even more popular.
American automakers of the time were already huge corporations with lots of complacent “old guard” executives who thought people would “buy American” just by virtue of them being American. Because they couldn’t pivot very quickly (or just didn’t want to) American cars of the time swiftly became hot garbage. Increased emissions restrictions and a lack of innovation led to underpowered, over complicated, and unreliable cars that were just as expensive, and often more expensive than their Japanese competitors.
This didn’t reeeealllly start to change until big boss dawg Lee Iacocca, then CEO of Chrysler, ordered the development of the Chrysler K Platform which released in 1981. (Incidentally, the wiki on the K car provides some good insight into your question as well: https://en.wikipedia.org/wiki/Chrysler_K_platform ) But by this time the reputation damage to American cars had already been done and “Japanese” became synonymous with economical and reliable in American culture. (Think of that scene in Back to the Future Pt. 2 where 1955 Doc is all disgusted at the "made in Japan" stuff and Marty says "all the best stuff comes from Japan!")
Another big factor is that Japanese automakers continued to produce comparatively cheap, reliable, high quality cars which solidified their good reputation while American companies remained spotty. There are some exceptions to the rule (GM’s LS and Vortec 4300 engines are widely regarded as “bulletproof.” American medium and heavy duty trucks were mostly exempt from emissions restrictions so were still high quality, etc.) but in general, you can buy any Toyota or Honda in their lineup, past or current, and sleep comfortably knowing it is probably going to last. If you’re buying American, you generally have to pay more attention to the individual reliability stats of the vehicle model and often even sub-model (different engines, transmissions, and such).
In regards to European cars, it generally doesn’t make a whole lot of economic sense for them to import cheap cars because import costs mean slimmer margins and our economy class market is just too competitive. That means they typically market themselves as luxury vehicles, and/or put themselves into a specific niche. (e.g. Volvos are the safest, Mercedes is the most luxurious and innovative, BMW offers the best driving experience, etc.) Because of that, we get fewer of the cheap, “tried and true” models from European brands and more of their fancy new stuff. Stuff that is new and fancy costs more to maintain and repair. Parts are more expensive and it can be difficult to even find someone who knows how to fix the car properly. Because European cars are more expensive and difficult to maintain, lots of people just don’t. When they don’t perform maintenance, the cars break. And when the cars break, they’re even more costly to repair. This leads to the general perception that European cars are more expensive and less reliable.
There’s also a general culture perception component as well, fair or otherwise… e.g. Americans see Germans as innovative, but with a tendency to over engineer things to a fault; Italians as passionate, but more focused on performance and aesthetics over functionality; and the Japanese as fastidious and hyper concerned with quality of reputation. These stereotypes are also applied to the goods they sell in American markets.
So at the end of it all, it really boils down to costs to purchase and maintain the vehicle, each manufacturers market niche, and the general public’s perception of the foreign culture, accurate or not. There is a general accuracy in thinking that Japanese cars are more reliable, as that is the focus of their more prominent brands, but there are always exceptions.
Thanks for coming to my LEM talk.
(edited for way too many commas and some other grammar)