Yes, there are two big reasons:

1) The Fed has made it clear that the injections are temporary and will be removed if the economy improves. Standard theory says that increases in the money supply expected to be temporary basically have no effect on inflation or (they lead people to want to hold more money). If you double the money supply but promise to reverse this in a year, the result is not huge inflation now till a year from now and then huge deflation, but no inflation (lots of people think about inflation as a differential equation, but this will lead you astray).

2) Near the start of the crisis in 2008, the Fed started paying interest on reserves which encourages banks to hold excess reserves, of which they hold a huuuuuuuuuuge amount. The interest rate is quite small, but this can have a huge effect this rate is above what banks can get elsewhere (risk adjusted). The appropriate interest on reserves could also easily be negative.