Should we "ignore" feelings while being mindful and aware of the present moment?

When I am not judging any moments of life and taking it all in, should I give importance to feeling anything at all? I tend to get very rational and "accepting" about things. A feeling of letting go arises, which makes me feel very passive? It feels like there is no time for a feeling because we are losing the next moments by living inside a feeling, either positive/negative. Also am I doing this right? Sometimes, it is like I am shutting that emotion up because I don't want to give in to a feeling. Why would I not want to give in to a feeling that makes sense at that point of time? That is mere repression. Any thoughts on this?