Can I interpret mean difference on a Likert scale as a percentage change I have pre-test data showing a mean of 3.71 for work-stress (7 point likert scale).
My post-test data shows a mean of 3.24 for work-stress (same 7 point likert scale). 
Paired sample t-test is showing significant mean difference at p < 0.001.
Can I interpret this drop in work-stress as  a $\frac{3.71-3.24}{3.71} = 12.7\%$ decrease in work-stress?
Some extra information: the pre test was a measurement before treatment and the post-test was measurement after treatment with 4 weeks time between pre- and post-test.
*the question on the likert scale were statements like: I often worry about work after worktime. (agree - disagree)
 A: Imagine that you labeled of the categories as:

1 - "Not at all", 2 - "a little bit more than nothing", 3 - "much less
  than average", 4 - "average", 5 - "VERY VERY VERY VERY VERY MUCH!!!!!"

Now, would you say that the difference between 3 and 4 is the same as between 4 and 5? Likert scale is ordinal, so it tells you only about the ordering of categories, not about the distances between then. So using means of Likert-scaled items as you described it would be inappropriate.
What you could do is to compare percentages of answers given in different categories. For example: "there was 5% increase in in rating XYZ as 'very good'", or "there was a 20% decrease in rating XYZ as 'good', or 'very good'".
Check also the following threads:
What are good basic statistics to use for ordinal data?
Does it ever make sense to treat categorical data as continuous?
Under what conditions should Likert scales be used as ordinal or interval data?
Moreover, you could also check Item Response Theory methods that are designed specifically for this kind of data.
