I know that elements with unpaired electrons are coloured especially the d-block element which can be explained by crystal field theory. But, why can't element with paired electrons give colour, is it because the energy gap is too large ?
Your assumption is wrong. There are elements with paired electrons which are coloured.
Colour is a product of electronic transitions in atoms or molecules. If those transitions match the energy of a photon of visible light, then the substance will be coloured (though there are some other rules about how intense the colour will actually be).
Some elements do show colour. Halogens, for example, exist as diatomic molecules in their native state and are all coloured. Chlorine is a greenish gas and bromine is an intensely red liquid. Sulphur is usually found as a yellow solid. All have paired electrons.