How (with what) would you fill this gap?

I have a gap that I left between old door frame and architrave (architrave is fixed directly to new tiles hence the gap in the thickness of the tile). I thought I will just fill it out with caulk/paint it and it will blend in with old door frame... However started filling the caulk , and that thing dries to semi squishable substance ( like an old chewing gum). I realize I should have put in a new Door frame to tie everything together nicely but that's no longer an option since everything is finished.

How would you fill this gap so that it's easily tied together with the old frame and would be paintable to match the old door frame?