It's an egregious allegation to make by saying Meade did not follow Lee's army after Gettysburg. In fact Meade did follow Lee and came very close to trapping him at the Potomac on July 13-14. It was only through a remarkable feat of bridge building and falling water levels in the river that Lee was able to escape prior to Meade's attack scheduled for the 14th. Meade's pursuit was remarkably effective given that he was under orders to protect Washington and Baltimore and had to move by forced marches on the east side of the South Mountain. Lee executed a very competent withdrawal. He never gave battle without a pre-planned and defendable line of retreat, the Shenandoah-Cumberland Valley being one of the best avenues of attack and retreat on the continent.
Recall that Grant failed to trap Bragg after the victory at Missionary Ridge, and that it took over eight months for Grant to bring Lee to bay at Appomattox. His Vicksburg campaign took six months. Grant captured the garrison, which never attempted an escape, and then paroled it. A few months later he found himself fighting the same troops at Chattanooga. Sherman's Atlanta campaign took four months and at the end of it he captured Atlanta, but failed to destroy the Confederate Army of the Tennessee.
Complaints about Meade and McClellan are really apologies for the first Republican administration to sell the American people a war that would be far more difficult to win than advertised. An added dimension in the case of Meade is that the Irish-Catholic was unacceptable as a hero for many Republicans who were Nativists and rabid anti-Catholics like the Beechers.