Re-coloring hair

I colored my hair red from a light brown /dark blonde color. Later that day, when the hair dried I noticed that there were patches of hair that were still the previous color. Like a one inch strand is half red half & half light brown, and there are patches of red and light brown. The roots are fine - they're red. When I was coloring the hair was completely saturated with the color. I've also colored my hair for several years and never had this issue, but it was the 1st time I went red. My question is... Would it be safe to recolor the part of the hair that didn't take the first time? I really don't want patchwork hair.