Hashem wants us to lean on Him only. Anything else we lean on, in the words of the prophet, is nothing more than a wobbly reed.
What does it mean to trust Hashem completely? It means that we sincerely believe that our salvation from any predicament is in Hashem's hands. It means that we lean on Hashem, and on Him only. So, when we lean on Hashem, we never fall and we're never disgraced.
Here's an example: Suppose that you're a soldier in combat and that your best friend has just been wounded seriously. You have to rush him to a waiting evacuation helicopter otherwise he'll be in grave danger. Your friend can’t walk, so he must rely on you and three of your fellow crewmen to carry him on a stretcher to the chopper. You and your buddies know that if you let him go for even an instant, he'll fall; you therefore grip the stretcher tight, because you're fully aware that his life depends on the four of you.
Hashem is a million times more compassionate than we are. Imagine for a moment that if a person truthfully and innocently leans on Hashem because he or she doesn't have the strength to deal with whatever they have to, do you think for a moment that Hashem will let you go? Never! All we have to do is strengthen our simple and uncomplicated trust in Hashem, and bingo! We're home free, we never fall.