Interpreting results so far:  "There is an overall difference between craving between groups averaged across all periods.  There is a difference across time.  The overall interaction with 7 d.f. is not significant."

Other comments:  You do not give enough detail.  So far, it sounds like a repeated measures design, not Multilevel. What are the elements, and what are their Ns?  How strong are those overall effects -- 0.001?  barely 0.05?

It is usually poor form (because it offers relatively little power) to analyze 8 time periods without considering useful contrasts instead of relying on that test across 8 periods.   A 1 d.f.  contrast that contains most of the trend or other differences will have far more power than the 7 d.f.  test among periods.  Testing the specific contrast also answers a specific question, like, "Is there a trend?" -- instead of giving a relatively useless answer like, "There are differences."

You say you "ran t-tests."  I have to guess, so I guess that you ran t-tests at the separate times.  The lack of "significant" tests here,whereas the overall test was significant, shows that you do have marginal power and that you cannot afford to waste power by testing the non-specific hypotheses.

Do you expect a linear time trend?  Was there a pre-intervention Baseline, which should be contrasted to the next period, to test an Intervention effect?  - An Intervention design might deserve a t-test  between 1 and 2 (assuming intervention after 1), to detect a jolt, with a separate test for 2 through 8 that tests for trend that might either return towards Baseline, move away, or stay constant.