That looks like repeated measures ANOVA
If you run all the tests seperately then you're not helping yourself - you are basically saying that each test is independent, unrelated, separate. With the ANOVA, you are saying from the get-go "Hold up 'ere pal, I'm going to do a bunch of tests; they're all important."
Now - if you do a planned comparison - select Bonferoni - then you can see differences between groups - not just a single over-all measure.
Bottom line - this is classic ANOVA - and you seem to have walked into the classic trap. If you google ANOVA/t-test and something like "why should I bother?" then it'll practically have your name and this data on it ... which is great because you'll get all the examples and explanations you could ever shake a stick at.