In ancient Asian languages there were no separate words for heart and mind, but one concept referring to both as an inseparable whole: heart-mind. In the East the image of a bird is often used to emphasize that developing a sharp mind and a compassionate heart need to be developed side by side.
Practising mindfulness does not only involve becoming aware of our experience as it is, but also cultivating of an inner attitude of compassion toward what is. So, it is not just about bare attention. We do not only open the eye but also the heart, even when what arises is painful.
When we sense that our striving to control the uncontrollable only contributes to more suffering, there is spaciousness for another attitude of kindness and compassion. Then, mindfulness can be deepened with heartfulness.
We do not have to practise the one before we can practise the other. Rather, the practice of opening the eye and the heart go hand in hand. When the eye opens, the heart responds and opens at the same time. When the heart opens, the eye sees more deeply.