I do not believe that God's call to lay our probem and concerns at His feet is a call to inaction but it is a call to not worry, to find joy in all things, and to listen for His voice. That's tough, though, for someone who wants to charge ahead, "fix" things, and never ask for directions. Once again, my "self" gets in the way.
Like I said, I believe I am making improvement in this area but, even when I give things up to Him, I need to fully give them up to Him. He doesn't want to hear my fretful jabber-jawing or teeth-gnashing about things that I have given up to Him. He has no reason to hear it; He knows my concerns. And, as for the people around me, well, they certainly don't want to hear it either! (Of course I am not discounting the importance of authentic close Christian relationships with others where you can share your concerns but what if, even in those relationships that I am blessed with, my focus could be more on the celebration of things I have given over to God rather than on re-hashing those things!)
Now, I am not a theologian and I hope I am not on shaky ground here but once I give my concerns over to God, I believe that He wants to hear my praise, my thankfulness for Him, my joy in all that I encounter ... not my continual fretting. I need to remember that.