Some contrasts:
Light vs Dark, light tends to come forward, dark recedes
Gray vs Saturated, saturated colors tend to come forward
Warm vs Cool, warm tends to come forward, cool colors recede
More Detail vs Less Detail, details tend to attract the eye. they don't bring things forward, but they do hold the viewer attention.
Since your tiles call for light background, you have to use other contrasts to pull the sprites forward. Reduce the contrast within the background elements, and increase the contrast in the nearer elements, and use warmer, and/or more saturated color in the nearer elements. Here is a thumbnail of a Bouguereau painting:
The figure is more saturated and has more details than the lighter background. Even the pale face has more color. Also notice the ground is a warmer color (yellow-ish stone) compared to the cool colors in the distance. Another trick is that the light foreground elements (skin) are completely surrounded by darker elements (shadow, hair, clothes), keeping them separate from the background, and coming forward (light on dark) compared to the darker elements.
Doing this with small sprites is not easy, but the principles are the same.
Hope this helps,
Tourist