Honda / Toyota advantage was cost. They produced a better product for slightly less money because they had lower production costs. If you look at early Toyota cars they where all low end and cheap because that's all they could make. Just look a the size of the Accord when it was introduced vs the Civic vs the Fit. It's all about starting at the low end of the market and working your way up to the less price focused customer.
PS: Don't forget the market decides price, you can only really control cost if you want to be more than a nitch player.
Yes but the Japanese strategy was not "sell at the lowest possible price". It was "we have good control over our costs, let's pick a price and see what we can deliver at that price". At that point in time, US automakers didn't even know what making a car cost them, they were so focussed on revenue they lost sight of the bottom line.
Car companies that tried to deliver a low-cost product without the quality behind it (eg Yugo) ultimately failed.