Meade had accomplished what no one else had, he destroyed the myth of Lee's invincibility and decided not to press his luck. His army was no doubt more difficult to handle than Lee's and if one element had walked into a trap and been destroyed, it would have wiped out all his gains. He probably found it incredible that Lee would just pack up and go home without trying to salvage something from his first appearance north of the MDL.
Keep in mind that losses on both side were about equal. Both had just over 23,000 killed, wounded, captured, or missing. That was a full third of the ANV, and a quarter of the AoP.
Lee had drawn his army into a strong defensive position, some say hoping for an attack by Meade, and it was raining quite heavily on 4 July. When Meade did not attack, Lee was able to withdraw in good order while keeping up a strong rear guard. If the ANV had been routed, then a strong pursuit would have been well justified. But against an army that was still in good order, in many cases spoiling for another fight, and well versed in defensive warfare, Meads decision to not mount a strong pursuit may have been a good one.
Also, Meade had only been in command of the AoP for, what, two days? before the battle? He didn't really know his army. His men, after three days of fighting, were short on supplies - including, somewhat ironically, shoes - and were not really in condition to face another stand up fight. Granted, the ANV was not in any better shape, but fighting with their backs to a rain swollen river may have given them the incentive to break the AoP.