I'm not sure where you are in the world and that will make a difference, but a few mistakes you've made are, first, you're trying to root these indoors, second, you've got them in what appears to be a tray rather than a deep pot, third, its not clear what you mean by 'picked up a couple of rose stems', fourth, you've not mentioned hormone rooting powder, which helps greatly with rose cuttings in particular. Depending where you are, it's likely the wrong time of year to take the cuttings too.
Cuttings should be freshly cut and taken once you are ready to proceed with inserting them into a prepared area outside or in a pot outside. You also need hormone rooting powder, and the cuttings themselves must not be 'woody', they must be from this year's growth.
The best way to propagate roses from cuttings is to take the cuttings in early Fall, when the weather is cooler (September in the UK), using new growth from this year. Each cutting should be around 8 inches long, you make a nick either side at the bottom of the stem, dip into hormone rooting powder, then insert into a pre prepared trench or piece of ground outdoors. Preparation of the area involves digging over and incorporating some grit if the soil is heavy, and the area shouldn't be in full sun, particularly not sun in the middle of the day. Alternatively, put the cuttings into pots and stand outside in a shady area. They should root over winter and start growing next spring.
A note of caution though - with some varieties, it will still be illegal to propagate yourself because the breeder's rights are still active, and second, a lot of roses are grafted onto a different rootstock to give them vigour; taking cuttings from such a rose might mean the rose you grow is not so vigorous or healthy.
The links below give more information
Finally, as I know you're struggling a bit with propagation techniques, it might be useful for you to look up the plant you want to propagate and read how to do it before you start, and that means for every single variety of plant. Or buy yourself a book or e-book on general propagation techniques like the one this link takes you to (available on Amazon too)