The way to do that is to mow it more often at a lower setting. What you are doing by letting it grow up tall is allowing the stems to lengthen. The blade of grass grows out from the end of the stem. When it gets up tall and you mow it back short, you're cutting off the entire blade and part of the stem. If you mow shorter the stems will become shorter. When you mow more frequently you will not have to cut as much off and you will not be cutting into the stems.

Does that make sense?