I believe that what Emerson means by saying that our age is retrospective is that we value thinkers and artists and heros of the past more than we value those of our own times. For example, we consider Shakespeare the greatest writer, Plato the greatest philosopher, and Michelangelo the greatest artist. One of Emerson's favorite themes is that there are more opportunities for greatness in the modern world, and especially in America, than have ever been realized in the past. He encouraged young people to live and work in the present and to create new ideas, new works of art, new inventions, new scientific discoveries, and new things that had never even been dreamt of in the past. He inspired many people to be creative in many areas. Walt Whitman, for example, was inspired by Emerson to become what many consider the creator of modern poetry. Emerson's most inspiring essay is "Self-Reliance." Another classic is "The American Scholar." Always he was encouraging young people to look to the future and not to the past.
Living in a "retrospective age" would be living among the ruins of past civilizations and feeling like a Pygmy descended from giants. This condition can be seen in India and even in Europe, but Emerson didn't want to see it happening in America.