In the modern Hasidic work, Netivot Shalom, R. Shalom Noah Berezovsky, the previous Slonimer Rebbe of Jerusalem, discusses the concept of how asking for our needs can be considered part of תפילה. His question is predicated on the equation of prayer with service of the heart (עבודה שבלב). If we are serving G-d through our words, it would seem antithetical to be asking G-d for our needs.
R. Berezovsky argues that part of prayer, based on the R. Chaim of Brisk’s famous essay on Rambam’s view of prayer, is to be focused on standing before G-d. When we are truly focused on where our prayers are directed, we bring about a connection between ourselves and G-d. As such, when we are pouring our hearts out the G-d, we are connecting to G-d, for we are recognizing that it is only G-d that can truly provide for our needs and remove our troubles.