I'd explain to him that you are reaching the limit of your knowledge and experience in web development and that you are not sure that you have the ability to create something nice enough to put your name on.

I completely understand how important it is to communicate skill ceilings to bosses and managers, but considering the OP communicated this once to their boss to no avail, and the fact that their boss also completely disregarded it, there's a chance their boss could simply say, "OK, so since you can't do the work, you can see yourself out."

Before OP busts in their bosses office about "I can't do this," maybe rethink this scenario and ask how important this specific task is to their future there and how they envision the work changing.