The Gemara of Rosh Hashanah (18;1) describes a case of two people who fell ill. Though they both had the exact same illness and both of them prayed to be healed, one of them recovered, while the other did not.
The Gemara questions what we would ask as well. Why is it that one's prayer was accepted while the other's was not. The answer given is that the one whose prayer was accepted prayed a complete prayer where as the other did not.
Rashi explains that a complete prayer refers to a prayer with total intent. We see from here that though they were equal in all criteria, the one meaningful difference between them was how they prayed.
We are told (Midrash Tanhuma Parashath Wayyera, 1) that G-d told the Jewish people: "Please be careful with your prayer, for there is nothing more beautiful than Tefillah and it is greater than all the sacrifices. Even if a person is not worthy to have his prayer answered and receive My kindness, once he prays to me with supplications, I will bestow My kindness upon him".
What an incredible gift! Let's use it and not fall in the trap of our evil inclination, which pulls us away in the wrong direction.