There are two problems with this statement. First, as I've already mentioned, it treats prayer as a last resort when it should, in fact, be our first response to life's trials. When troubles come our way, our immediate reaction should be to ask for God's help and intercession in the matter. Unfortunately, our gut reaction is typically to figure out how to handle the situation on our own, and then, when that fails (as it always will), we resort to prayer.
The second problem with the statement is that it treats prayer like the fat kid who gets picked last for the neighborhood ball game. We act as if prayer has no power, like we're doing it simply because we know it's the right thing to do. But if we pay attention to what the Bible has to say about prayer, we would realize that it is powerful. It can change situations, alter lives and so much more. Prayer is big. It is strong. It is a vital part of our existence, and I believe it's a slap in God's face when we treat prayer as a last resort. After all, prayer is our means of communication with Him, so if prayer is weak or ineffective, that means God is weak and ineffective.
Are you facing challenges today? Does life have you confused, frustrated or feeling hopeless? If so, I urge you to pray. Don't try to figure things out. Don't try to make sense of the situation. Don't seek the aid of people, pills or other worldly comforts. Instead, as soon as the problems arise, run to Jesus. Talk to Him. Pour out your problem. Then listen for His response and feel the sense of peace that pours over you as He assures you that He can handle anything you bring to Him.
Prayer is not a last resort, or at least, it shouldn't be. If we really want to solve our problems and restore the peace in our lives, we need to pray, and we would do well to see prayer through the eyes of God instead of through our warped lens of inferiority. Prayer can move mountains, heal the sick and comfort the brokenhearted but only if we don't limit its power.
Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much. - James 5:16