It is true that we are connected by collective Karma. I was once told by a devote Buddhist that whoever we meet in this existence is someone we either owe or someone who came to pay back.
That sounded awfully scary for me to even wish to meet any more new people. But as a Buddhist we cannot escape our karma and if certain aspects of your karma do not arise in this life, we will carry it forward to the next life during which time we enhances it.
Learning the Dharma makes me realise that our karma can change, virtuous deeds leads to either gaining positive karma and bad deeds to negative karma. Therefore with even the slightest knowledge of karma, we are in control of our life and can do something with our karma.
After reciting any puja or doing something beneficial, we dedicate the merits collected to others. Such being the case, I feel it is logical that we can dedicate our merits to our parents who gave us life and also brought us up.
As mentioned by Yontenjamyang, the best is for your parents and loved ones to practise Dharma. Nothing can beat this method.