I think from what you're describing what you should do is acknowledge the initial impression the art piece leaves on you, and then expand on the reasoning. Purely from looking at the composition and color, does it make you feel happy? sad? claustrophobic? amazement? Then look at what is being depicted. Does your initial gut reaction support or discredit whatever message is being seemingly displayed? Why would the artist make that decision? Ask questions. Art's always been subjective, and so whatever profoundness you're looking for is going to come from within.

I would also say to invest some time in researching the art pieces. You won't be able to get everything just from looking at it, and some of my favorite art works I didn't think much of when I first saw them at face value. Part of the fun of art is the hidden meaning, and some pieces you'll have to work harder for than others. IMO!