Rebirth

If we are bound by our karmic deeds, ie. If we have good karmic deeds, we will attain salvation, if we have bad karmic deeds we will be reborn, how does prayer tie in. Does it mean if we are loyal devotees and pray at every given moment, but our actions are not good, will we still be reborn? If yes, does that not mean that the karmic laws are useless, it it not unjust? And if no, what about a person who has the most purest soul and does not harm an ant, but does not believe in prayer? Will they be reborn, how is that just? I personally believe that it is not in our prayer but our hearts and actions, but am I in any way wrong for believing this?