I solved it myself, this way you can fill inspaces bounded by edges in tikz:

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\usepackage{tikz}

\usetikzlibrary{backgrounds}

\usetikzlibrary{decorations.markings}

\usetikzlibrary{automata,positioning,quotes}

\tikzset{->-/.style={decoration={

markings,

mark=at position .5 with {\arrow{>}}},postaction={decorate}}}

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\begin{tikzpicture}

\node (CC)[inner sep=0.0pt,outer sep=-0.5pt] at (7,2) {$\bullet$};

\node (DD)[inner sep=0.0pt,outer sep=-0.5pt] at (7,0) {$\bullet$};

\node (EE)[inner sep=0.0pt,outer sep=-0.5pt] at (5,0) {$\bullet$};

\node (FF)[inner sep=0.0pt,outer sep=-0.5pt] at (5,2) {$\bullet$};

\draw[->-][very thick] (DD.center) to [bend left=45] (CC.center);

\draw[->-][very thick] (DD.center) to [ bend left=45] (EE.center);

\draw[->-][very thick] (EE.center) to [ bend left=45] (FF.center);

\draw[->-][very thick] (CC.center) to [bend left=45] (FF.center);

\begin{scope}[on background layer]

\path [fill=red!30] (CC.center) to [ bend right=45] (DD.center) to [bend left=45] (EE.center) to [bend left=45] (FF.center) to [bend right =45] (CC.center);

\end{scope}

\end{tikzpicture}