Verses 1-7 are reminiscent of the poem in the previous chapter. He recognized that he had not pulled himself up by his own bootstraps. He knew that God had lifted him up and blessed his life. True, David was called the sweet psalmist of Israel, but who really deserved the recognition for his wonderful poetic contributions to the Hebrew hymnbook? To quote David himself, he said, "The Spirit of the LORD spoke by me, and His word was in my tongue." David understood well enough that God was responsible for his success.
Now, God doesn't do everything by overt spiritual means nor by mysterious supernatural intervention. Often, He works through simple physical means. (Maybe "simple" isn't a proper description of David's 37 mighty men). With men like those doing the kinds of things that they did for David… no wonder he was such a success.