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Let $G$ be a commutative group and $\mathbb{C}$ the field of complex numbers, $\mathbb{R}^{+}$ the set of positive real numbers and $f,g,h,k:G\times \mathbb{R}^{+}\rightarrow \mathbb{C}$. In this paper, we first consider the Levi-Civitá functional inequality $$\begin{eqnarray}\displaystyle f(x+y,t+s)-g(x,t)h(y,s)-k(y,s)\leq {\rm\Phi}(t,s),\quad x,y\in G,t,s>0, & & \displaystyle \nonumber\end{eqnarray}$$ where ${\rm\Phi}:\mathbb{R}^{+}\times \mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ is a symmetric decreasing function in the sense that ${\rm\Phi}(t_{2},s_{2})\leq {\rm\Phi}(t_{1},s_{1})$ for all $0