In this paper, we use the logarithmic derivative lemma for several complex variables to extend the Milloux inequality to differential polynomials of entire functions. As an application, we subsequently apply the concept to two Picard-type theorems: (1) Let $ f $ be an entire function in $\mathbb{C}^{n}$ and $a, b\;(\neq 0)$ be two distinct complex numbers. If $ f\neq a, {\cal{P}}\neq b, $ then $ f $ is constant. (2) If $ f^{s}D^{t_{1}}(f^{s_{1}})\cdots D^{t_{q}}(f^{s_{q}})\neq b $ and $ s+ $ $ \sum_{j = 1}^{q}s_{j}\geqslant 2+\sum_{j = 1}^{q}t_{j}, $ then $ f $ is constant, where $ D^{k}f $ is the $ k $ -th total derivative of $ f $ and $ {\cal{P}} $ is a differential polynomial of $ f $ with respect to the total derivative.