CIC Filter vs Simple Downsampler
If you are only decimating by four, then a CIC filter is not the way to go.  CIC filters have two advantages and one big disadvantage.  The advantages are that they don't require any multipliers, just (large) adders, and they can efficiently decimate by really large factors.  The no-multipliers advantage was a big deal years ago when multipliers were expensive and not always available, but they are cheap now.  And since you are only decimating by a factor of 4, the ability to decimate by large factors does not help you either.

The one big disadvantage of CIC filters is that their frequency response is not flat in the pass-band, so designers usually put a FIR filter after the CIC filter whose primary purpose is to compensate for the CIC filter's non-flatness.

My advice would be to continue decimating with one or two FIR filters, though I would recommend using a better filter than [1 5 10 10 5 1].  Try using Matlab's fdatool or Matlab/Octave's "fir1" command to design a better filter.