What is complement of Context-free languages?
One can understand your question in two ways, according to the definition of "the complement of CFL".

case A: Complement of CFL is the class of all the languages that are not in CFL.  Formally, $$\overline{CFL} = \{ L \mid L\notin CFL\}.$$
In that case, $\overline{CFL}$ is way bigger than $P$, it even has languages that are not in $R$, etc.
But maybe that's not what you meant.

case B: Define the complement-CFL class as $$co{CFL} = \{ \bar{L} \mid L \in CFL\},$$
in words, the set of all languages $L$, such that $L$'s complement is context free.

In that case, what you wrote makes sense: 
$CFL \subsetneq P$  (by the CYK algorithm), and also $co{CFL} \subseteq P$ (run the same algorithm, output the opposite answer), and since $CFL \neq co{CFL}$, 
then it should be immediate that $co{CFL}\subsetneq P$, right?