Inflation only really affects dollar-denominated accounts that don't bear (enough) interest. Everyone needs to have some money in such accounts (checking accounts, cash) for short-term spending purposes. For poor people, this is usually the majority of their holdings; for wealthy people, it will only be a tiny fraction. Thus, inflation has a larger impact, percentage-wise, on the poor. Inflation also produces downward pressure on effective wages, since workers have to keep getting raises just to maintain parity.

I think that inflation is dramatically higher than is commonly realized; increased production efficiency should be causing the prices of most things to plummet, but other than electronics, that isn't happening.