The Gettysburg Address was not a post-battle speech in the sense that I believe you are viewing it in. It was a dedication speech for the Soldiers National Cemetery at Gettysburg, where thousands of the Federal dead were buried that fall (and accidentally, a few Confederates), and should be viewed in that context.

Almost immediately after the two armies left Gettysburg, two prominent Gettysburg citizens, David McConaughy and David Wills, started buying up private property to preserve the land as a living monument to the Federal dead (the beginning of the current Gettysburg National Military Park), and to establish a cemetery for the Union dead adjacent to the Evergreen Cemetery on Cemetery Hill (the hill having been the key to the Union's position during the battle).

A dedication ceremony was planned for the fall, and the organizers determined that a prominent figure should be invited to deliver an address at the ceremony. They were able to secure the most prominent orator in the nation - Edward Everett.

Because the cemetery was a national cemetery, it was determined that an invitation should also be sent to Lincoln, as President of the Union, inviting him to formally set aside the grounds with a "few appropriate remarks." Lincoln accepted the invitation, considering it an opportunity to deliver a political speech that connected the sacrifice of the soldiers, the cause of the Union, and the emancipation of the slaves.

After Everett's address of two hours, Lincoln made his speech, which lasted only two minutes. He connected the establishment of the nation to the Declaration of the Independence, rather than the Constitution, and declared that they could not consecrate the ground of Gettysburg any more than the soldiers had, and could only truly honor them by dedicating themselves to winning the war, ensuring freedom for all, and saving republican government for posterity.

The speech was well-received by the audience, but Lincoln did not think it accomplished what he had set out to do. It was not until the months that followed and the years that followed that the speech began to be appreciated as the masterpiece that it is now considered to be. Everett himself wrote to Lincoln, "I should be glad if I could flatter myself that I came as near to the central idea of the occasion, in two hours, as you did in two minutes."