Paint the unfinished drywall with a coat of primer.
Use masking tape to create a pattern on the new wall that mimics the pattern of the mortar joints in the basement walls, if the basement walls are cinder block.
Inspect the colors of the basement walls. Concrete often consists of multiple, irregular shades of gray. Also look for subtle color tints in the grays.
Mix black and white in multiple containers to create a range of matching gray shades. Add a few drops of color to a few shades, if color tints were observed in the basement walls. Use a matte paint if the basement walls are unfinished. Use a glossier paint if the basement walls are sealed with concrete finish.
Sponge the colors onto the wall in a mottled, irregular pattern. Blend and overlap each patch slightly to create a unified appearance.
Remove the tape, if a mortar joint pattern was created, before the paint dries. Allow the paint to dry. Create a paint color to match the mortar between the concrete blocks. Paint inside the spaces where the tape was removed using a smaller, artist’s paintbrush.