Analysis of internal customer response

What you are talking about is a Likert scale.
Now, about your analysis. You do not have a big smaple, so a point estimate of your averages is not apporpriate. You need to put a confidence interval around your estimates to identify any real changes.
I have often seen statements like: “Last month the average was 3.09, and this month is 3.02. This can be attributed to a change in management.”
What a crock. This is hogwash. There is no reason to believe that this is natural variation. Of course the score will change from time to time, but is it significant? Even if it is not significant at the .05 level, you might be prompted to make some claim about the change. This can be reasonable if there is a trend in the statistics over time.

It’s a mistake to try to apply correlation in this case.  ANOVA might be somewhat applicable but just barely.  You have ordinal data you’re trying to analyze with “normal” techniques.  The two shouldn’t be mixed in such a way.  If you feel you must put numbers to these, you would be better off using non-parametric analysis.  But the best way to analyze would be to simply chart the responses in a pie chart or bar chart.  You still need to do the “heavy lifting” when it comes to understanding why you receive scores in the lower categories to understand what is going wrong (as well as in the higher categories to understand what you are doing right).  Playing with ANOVA or correlation won’t help you in that respect.