special relativity - Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$ \partial_\mu \mathcal{L}=0~? $$

If this is the case doesn't the above equation imply that $\mathcal{L}$ is a constant? I know that $\mathcal{L}$ is a functional not a function but at the end it is still a function of space-time.