I'd say no. It doesn't specify, but I'd think most likely no.

My grounds are that entangled gives you a penalty to your dex. If you were flatfooted, it would instead say that you are denied your dex. While it could possibly both deny dex and give a penalty, its extremely unlikely.

Also of note, for all intents and purposes, entangle from web is the exact same entangle as the entangle spell. The only difference is that a web can block line of sight and line of effect due to its 3 dimensional nature and opacity.