We performed electrical resistivity and ^{13}C nuclear magnetic resonance (NMR) measurements on $\lambda$-(BEDSe-TTF)_2FeCl_4 under various pressures to obtain insights into the effect of $\pi$-d interactions on the antiferromagnetic (AF) phase. The resistivity shows that the insulating state is maintained up to 2.0 GPa. ^{13}C NMR measurements reveal that the AF transition occurs at 28, 31, and 23 K under 0.5, 1.0, and 2.0 GPa, respectively, indicating that a single AF phase in $\lambda$-(BEDSe- TTF)_2FeCl_4 is observed under various pressures, whereas two AF phases were observed in $\lambda$- (BEDSe-TTF)_2GaCl_4. The difference in phase diagrams between the magnetic anion salt, $\lambda$- (BEDSe-TTF)_2FeCl_4, and the non-magnetic anion salt, $\lambda$-(BEDSe-TTF)_2GaCl_4, is attributed to $\pi$-d interactions. These results provide insight into a possible microscopic role of $\pi$-d interactions in the Fe salt. The magnetic properties of -(BEDSe-TTF)2FeCl4 are described by the isolated cluster comprising two dimers and two anions with positive and negative $\pi$-d interactions, suggesting antiferromagnetic coupling between two dimers in the cluster. We also discuss the possible AF structures of $\lambda$-(BEDSe-TTF)_2FeCl_4.