Ivy stems?

Novice here.

I'm planning on sowing a new lawn before the autumn's out and have spent the last couple of weeks manually removing all the big weeds and unwanted shrub roots from the soil (it's a big garden, so quite time consuming). However, I find that I am left with lots of these thin green / light brown stems, which I think are common ivy stems (though I may be wrong).

When I look around the garden, there are hundreds of the blighters still in the soil (sorry, the picture isn't great, but you can see a couple of them just in front of the secateurs).

I wanted to rotavate at the weekend. Is it necessary to removal ALL these stems before I rotavate? Given there are so many of them, it would take for ever to do it manually (and I don't particularly want to use weedkiller). Would it be worth rotavating first and then clearing any stems that are still showing afterwards?

Thanks.

 

I think if it gets chopped up you might get away with it, but best to remove all the stems you can, the roots are not a problem.