Personally I'd probably be fine if somebody presented this to me and said, overall this is significant, and the bar diagram shows what is responsible for the significance, so I wouldn't require additional formal tests.
However, you may want to do them anyway. Here is what you can do. There are seven ways to split the four levels of age in two classes (1 vs 234, 2 vs 134, 3 vs 124, 4 vs 123, 12 vs 34, 13 vs 24, 14 vs 23). You can run 2*2 table chi square tests for any of these comparisons. In order to take into account multiple testing, you can use the Bonferroni correction for 7 tests, i.e., for testing at 5% level, compare the p-values with 0.05/7.
Problem with this (as generally with multiple testing) is that it loses some power. If you end up with p-values between 0.05 and 0.05/7, you may want to say that this is suspicious, though not significant. But if your data set is of a good size (i.e. not too small, and not so big that everything will always be significant) and the true situation is rather simple (in the sense that either something strong is going on or nothing), all tests or at least those you care for may well either be significant using 0.05/7 or insignificant even using 0.05.
PS: A slight improvement is Bonferroni-Holm: Compare the smallest p-value with 0.05/7; if that's significant, compare the next smallest with 0.05/6, then 0.05/5 etc., until something is insignificant.