Dots on a Page?

I played the flute in my high school band, and I feel like I learned a lot about music from my band director.  One of the things he always used to say to us was "Stop playing the music as if it were just dots on a page".  He meant that we were playing all the right notes and rhythms, but that's all we were doing.  Even when you play a piece perfectly as far as mechanics go, there is still more that you need to add to it.  Hitting the correct notes, playing to appropriate tempo, and following the correct dynamics are all very important, but that is not all music is about.  I could probably sight read an easy song perfectly, but if I didn't really connect with the song or know what it was about, then it isn't quality music making.  When the performer is really feeling the music, and feeling the emotion behind the song, then it sounds better.  I know that at a concert, I would rather the musician be really into the song and make a few mistakes than play it perfectly but emotionlessly.  Even computers that can create "perfect" rhythms are manipulated to sound more human-like, as Levitin pointed out in chapter six.  Music is not about perfection-although that can help.  It is about human involvment.  Just playing "dots on a page" is not enough.  A performer has to truly understand and connect with the song he or she is playing.  So my question is, how can  we hear the difference between simply playing  "dots on a page" and something by a more emotionally connected performer?  We know it's there, but how does emotion translate into something audible?