In the markets where the money did end up, like the stocks and bonds markets, inflation ran rampant with NASDAQ and S&P history shows.
And neither S&P nor NASDAQ had anything resembling rampant gains, BTW:
S&P: https://www.macrotrends.net/2526/sp-500-historical-annual-re...
NASDAQ: https://www.macrotrends.net/1320/nasdaq-historical-chart (you have to click on the "by year" tab).
In neither of these charts a person unaware of QE could identify a trend.
Inflation as in the rise in price of a basket of goods is generally used in reference to the consumer price index, but can also be used in reference to stocks, and baskets of those such as the indices.
If the prices of assets rise, that is appreciation. If stocks or houses appreciate, you can sell them and profit: Your purchasing power rises. If consumables experience inflation, you can not sell them for a profit: They are either immaterial, like services, or can rot, like food. This isn't pedantry, these are different concepts.