McDowell was certainly outnumbered after General Johnston's army arrived on the field.
If General Patterson, who was in command in the Shenandoah Valley, had been able to engage or detain Johnston, the fate of the day might have been different.

But Johnston outgeneraled Patterson, and achieved what military genius always does,--he had his force in the right place at the right time.
The effect of the Rebel victory at Bull Run was at once visible in the rigorous policy adopted by the Confederate Government.

The people of the Confederacy knew that their numbers were less than those of the Union, but Jefferson Davis had in effect told them that fifteen Southern men might be relied upon to put to flight thirty-five Northern men, and on this ratio they felt equal to the contest.

The Congress at Richmond went to every extreme in their legislation.

A fortnight after the battle they passed "an Act respecting alien enemies," "warning and requiring every male citizen of the United States, fourteen years old and upwards, to depart from the Confederate States within forty days from the date of the President's Proclamation," which was issued on the 14th of August.
Those only could remain who intended to become citizens of the Confederacy.