Only the tav (ת) in תפילה implies that either you are the one causing the falling or that you are commanded to fall.
During the birth of my son last shabbath, I told my wife the reason the birth was taking so long was not because it needed to, but because we needed to pray for all the others around us in the hospital giving birth at the same time.
A few minutes later, I was learning in the Noam Elimelech and came across a Torah about how Tzaddikim fall because HaShem makes them fall, in order that when they pick themselves up again, they can raise all the other fallen around them as well.
The nature of Tefillah is directly related to falling--when we are in a tight spot, when we have fallen, we were put there to raise ourselves up again through sweet prayers to HaShem, our Father.
Sometimes we fall because of our own actions, sometimes we fall because of extenuating circumstances, but why we fell isn't important--the purpose of our fall is what is important--we fell in order to pick ourselves up, to raise up those around us as much as ourselves. We are all responsible and mixed up (ערבים זה לזה) with one another. [See this post for much more on this idea.]
There is one more way to read the word תפילה and that is as an acknowledgement that You HaShem made me fall. You brought me low, so that I could receive Your salvation, so that You could redeem me Yourself and express Your love for me.
This is why tefillah has to always come from a place of deep joy--because we know the good is already on the way.