The Prophet SAW said in the hadith recorded by At-Tirmithi and others:
The invocation of my brother, "None has the right to be worshipped save You;glory be to You, far removed are You from any imperfection; I have been amongst the wrong-doers," ( translation of the Ayah you have given ) none who is experiencing difficulty employs it except that Allah SWT would relieve him of his difficulty.
The first part stating "none has the right to be worshipped save You" affirms Tawhid al-ilahiyyah. Good can only be procured by the will of Allah (swt), everything He wills, is, and everything He does not will, is not. The obstacle to this good on the part of the servant is his sins, anything else that is outside the ability of the servant occurs by the decree of Allah (swt).
The second part stating "...I have been among the wrongdoers" makes the supplicator acknowledge and repent to Allah (swt) of his/her sin/s. Mankind was created weak and we all sin, but Allah (swt) loves and forgives those who keep turning to Him in repentance confessing and asking ONLY Him for forgiveness.
In a nutshell, testifying tawhid (oneness of Allah (swt) and associating NO partners with Him) opens the door to good in your life and asking for forgiveness from Him closes the door to evil in your life. Harm touches a believer because of his/her sins and asking for forgiveness from only Allah (swt) removes the cause of harm which is the sin/s.
Allah (swt) knows best..
May Allah (swt) give you the best of this life and the next