Mukai and Sakai proved that given a vector bundle$E$of rank$n$on a connected smooth projective curve of genus$g$and any$r$∈[1,$n$], there is subbundle$S$of rank$r$such that deg Hom($S, E/S$)≤$r$($n−r$)$g$. We prove a generalization of this bound for equivariant principal bundles. Our proof even simplifies the one given by Holla and Narasimhan for usual principal bundles.