You might try doing chordal analyses. You basically stack all the harmony notes into the intervalsl of 3rds; the lowest note will then be the root of the chord. There's more than that to it, depending on how deeply you want to delve into it. Surf the internet for information on how to perform chordal analyses, and/or read Stefan Kostka's Tonal Harmony. It's a very important skill within the realm of music theory and ultimately, piano playing. The left hand often plays the majority of the harmonic elements, and could perhaps be memorized through looking from that standpoint. Try writing the chords in roman numeral form underneath the bass staff and reciting the chords aloud while you play.