High-powered money is another term for the monetary base or MB. MB represents all money created by the government. However, that is not all the only source of money. Banks are allowed to create money too. Which is why higher aggregates like M2 and M3 are greater than MB.
Because bank money is greater than government money, it (and not MB) is more of a primary determinant to monetary inflation. Pretend there is an economy of blue dollars and yellow dollars. The blue are created by the government and the yellow by banks. There are many more yellow dollars than blue dollars. So when the supply of blue dollars goes up it doesn't matter as much because of the number of yellow dollars.
Bank money was being destroyed in the crisis which was actually creating deflationary pressures. The collapse in higher monetary aggregates was offset somewhat by the surge in the monetary base.
Now typically base money is used to create and leverage higher aggregates, but this was not the case during the crisis. Because of liquidity concerns, banks curtailed monetary creation so this is why inflation did not happen.