  We prove a Ne\v{c}as-Lions inequality with symmetric gradients on two and
three dimensional domains of diameter $R$ that are star-shaped with respect to
a ball of radius $\rho$; the constants in the inequality are explicit with
respect to $R$ and $\rho$. Crucial tools in deriving this inequality are a
first order Babu\v{s}ka-Aziz inequality based on Bogovski\u{i}'s construction
of a right-inverse of the divergence and Fourier transform techniques proposed
by Dur\'an. As a byproduct, we derive arbitrary order estimates in arbitrary
dimension for that operator.
