Power depends on voltage across the circuit and resistance of the circuit

\begin{equation}
P = \frac{V^2}{R};\\
P_{series} = \frac{V^2}{(R_1+R_2)};\\
P_{parallel} = \frac{V^2}{(R_1^{-1}+R_2^{-1})^{-1}}=\frac{V^2}{\frac{R_1R_2}{R_1+R_2}}=\frac{V^2(R_1+R_2)}{R_1R_2};\\
\frac{P_{series}}{P_{parallel}} = \frac{R_1R_2}{(R_1+R_2)^2}
\end{equation}

Since $R_1$ and $R_2$ are always positive, $R_1R_2 < (R_1+R_2)^2$
i.e. $P_{series} < P_{parallel}$