Simply \stackunder{tabular content}{text}. If the text is more than a line, it can be incorporated into a \parbox, as shown in my 2nd MWE.
\documentclass{article}
\usepackage{stackengine}
\begin{document}
\begin{table}
\caption{Model selection metrics}
\begin{center}
\stackunder{
\begin{tabular}{l c c c c c}
\hline
{} & {\itshape BIC} & {\itshape AIC} & {\itshape CAIC} & {\itshape HQIC} & {\itshape Correlation}\\
\hline \hline
Linear Regression & 138,210 & 138,014 & 138,236 & 138,080 & 0.2759\\
2-class (restricted) & 134,442 & 133,982 & 134, 503 & 134,135 & 0.2970\\
3-class (unrestricted) & 134,437 & 133,977 & 134,498 & 134,131 & 0.9275\\
3-class (restricted) & 134,128 & 133,464 & 134,216 & 133,685 & 0.2001\\
3-class (unrestricted) & --- & --- & --- & --- & --- \\
4-class (restricted) & 134,088 & 133,221 & 134,203 & 133,510 & 0.3045\\
4-class (unrestricted) & --- & --- & --- & --- & --- \\
5-class (restricted) & 134,160 & 133,089 & 134,302 & 133,446 & 0.3087\\
5-class (unrestricted) & --- & --- & --- & --- & --- \\
\hline
\end{tabular}
}{\footnotesize Note: preferred model for each metric in \textbf{bold}.}
\end{center}
\end{table}
\end{document}

For an extended note, place the under-text in a \parbox:
\documentclass{article}
\usepackage{stackengine}
\begin{document}
\begin{table}
\caption{Model selection metrics}
\begin{center}
\stackunder{
\begin{tabular}{l c c c c c}
\hline
{} & {\itshape BIC} & {\itshape AIC} & {\itshape CAIC} & {\itshape HQIC} & {\itshape Correlation}\\
\hline \hline
Linear Regression & 138,210 & 138,014 & 138,236 & 138,080 & 0.2759\\
2-class (restricted) & 134,442 & 133,982 & 134, 503 & 134,135 & 0.2970\\
3-class (unrestricted) & 134,437 & 133,977 & 134,498 & 134,131 & 0.9275\\
3-class (restricted) & 134,128 & 133,464 & 134,216 & 133,685 & 0.2001\\
3-class (unrestricted) & --- & --- & --- & --- & --- \\
4-class (restricted) & 134,088 & 133,221 & 134,203 & 133,510 & 0.3045\\
4-class (unrestricted) & --- & --- & --- & --- & --- \\
5-class (restricted) & 134,160 & 133,089 & 134,302 & 133,446 & 0.3087\\
5-class (unrestricted) & --- & --- & --- & --- & --- \\
\hline
\end{tabular}
}{\parbox{4.6in}{
\footnotesize Note: preferred model for each metric in \textbf{bold}.
However, if my note is particularly long, I can just place the note in a parbox.}
}
\end{center}
\end{table}
\end{document}
