The human brain is a complex organ and why you do what you do, at any given time, depends on the circumstances and how you feel about them. To examine why you may feel anxiety after exercise, you have to look at the various theories on how human beings interpret experiences and emotions.
How Brain Processes Experience
When you experience a stimulating event, your brain begins to process and organize the information into emotional and physiological responses. Your brain has centers that manage emotional experiences. The thalamus and amygdala are connected with emotion as well as the autonomic nervous system. Thus, when your body responds automatically to some event, such as exercise, a flood of emotions may be triggered.
In looking at why you may feel anxious after exercise, you need to consider your body's natural reaction to physiological signals. In 1927, Walter Cannon created his own theory of emotional response. He believed that you experience a situation, then feel an emotion that leads to a physiological response. In the case of exercise, the situation is one of movement and exertion, which could lead to anxiety, following Cannon's theory, because the physiological response is to run away from danger when muscles are tense and in use.
James Lange proposed quite a different theory of emotional response in 1884. He was working with psychologist William James, and together they postulated the idea that the arousal associated with an event causes humans to interpret an emotion. So in the case of exercise, you would feel anxious if you were to misinterpret the arousal and muscle use caused by exercise. In a sense, you would have mistaken exercise for the need to "fight or flight," like a challenged animal, thus creating anxiety.
Cognition and Emotions
Both the Cannon Theory and the James-Lange Theory suggest that human bodies signal a response before the mind can catch up. Cognitive theorists such as Richard Lazarus believe that after an event, you cognitively process it, which then leads to arousal and emotion at the same time. So, if after exercise, your brain processes your physical state as one of needing to be active or run away, the emotion to follow could be anxiety.
What can you take away from this? Learn to use the sensations and perceptions you feel as a starting place; then allow your brain sort out if you truly are in danger or merely experiencing the aftermath of an exhilarating workout. In this way, you will not likely misinterpret an innocuous event, such as exercise, as a fight-or-flight situation.