When F-Value of treatments are not significant, researcher could be used Duncan test. Probably you find a little differences in Post-hoc Duncan test but it is completely depend on researcher opinion. Please look at "Statistical desighn in agricutural research" book by Dr. Yazdi Samadi and et al., "Compare mean treatments" chapter.
I would advise to look at the structure of the variable data (i.e. if they follow normal distribution, the real meaning of the potential significance, etc.).
My problem is that in one of our manuscript the ANOVA was not significant for 7 traits, however when Comparison of Means was performed using Duncan multiple range test, some of those traits showed significant difference among means.
Now one of the reviewer asked that "you are not permitted to use Comparison of Means when ANOVA is not significant" and "you have to remove all figs and data and text accordingly".
I am sure he is wrong, but he insisted on his comments. I just wanted to more scientifically convince him.
I think we have to show the significance of our works in every window working and that is available, this is happening with more accurate Duncan or LSD test instead of F test