When you print money you devalue existing money, if the holders of the existing money keep holding it, keep trusting it, the devaluation is much smaller.
The inflation if visible in asset prices, eg. a painting would sell for half a billion dollar, all these companies being evaluated at billions of dollars, now holding billions of $ as state reserve doesn't look so big anymore.
Unless those billions in asset price increases buy less consumables than they did before QE, there isn't any inflation in the US yet, it just means Americans are richer.
The inflation if visible in asset prices, eg. a painting would sell for half a billion dollar, all these companies being evaluated at billions of dollars, now holding billions of $ as state reserve doesn't look so big anymore.