  In this note, we show that \cite[Corollary 3.2]{sad} is not always true. In
fact, we characterize essential left $\phi$-contractibility of the the group
algebras in the term of compactness of its related locally compact group. Also
we show that for any compact commutative group $G$, $L^{2}(G)$ is always
essentially left $\phi$-contractible. We discuss essential left
$\phi$-contractibility of some Fourier algebras.
