That pattern you see requires a basic cross stitch technique. See image below and instructions...
Thread a needle with three strands of red embroidery floss. Starting at the flower's center, bring the needle up from the back of the fabric and make your first stitch, leaving a 1"-long tail of thread. Make the next few stitches over the tail. (this will secure the tail without creating a bulky knot.) Continue filling out the design. When thread runs short, pull your needle through the last stitches and clip ends short. Rethread and stitch to finish.
I tried to scan the pattern you can use for your pillowcase.
