Now, one of the assumptions underlying ANCOVA is that the within group regression slopes are equal (i.e. for both men and women).
What the significant interaction term is indicating to you is that there is a slope/treatment interaction i.e. the regression slopes are different for men and women, and thus, you’re violating the assumption of homogeneity of regression slopes.
Your approach of conducting separate analyses is appropriate, however, if needed there are other options such as the Johnson-Neyman procedure.