For my sequences I got Tajima's D value as -0.94880 and P > 0.10. I was wondering if I could use this results to claim that the test of neutrality is negative and the molecule under consideration is under selection pressure?
A negative Tajima's D value is usually interpreted as purifying selection, or as a signature of a recent population expansion.
You didn't explain how you calculated the p-value, so it is difficult to interpret it. It seems that it is higher than 0.10, so not significant. You should plot the distribution of Tajima's D on the rest of the genome (or at least the same chromosome), and see where your value falls.
Here we are having a conflict. While Tajima'D and Fu's are significant and negative, our BSP indicates a no recent event of population expansion but constant size. We used D-loop and ~1000 sample size for a single population. Do you know why this conflict ocurrs?