The best way to alter a single color like this on a simple image such as this is to alter the Hue and Saturation [CTRL / CMD + U]
...
This allows you greater color control and keeps the anti-aliased edges of the image intact.
Most beginners alter colors like this by simply selecting the color with the wand, or using the paint bucket on the color. Unfortunately this usually does one of 2 things:
- Makes the ragged edges that you saw.
- Leaves a halo of the old color as an orphan.
I did this in a few seconds with that tool: