Translation:I had to go out because I felt bad.
It's a common misconception that you should always use badly and well with the verb to feel. However, it depends on the context. If you burned your fingertips in the campfire and couldn't put the marshmallows on the roasting stick, you could say you were feeling badly; your ability to feel with your fingers was compromised because they were injured. If you're talking about being sick, you would say, "I feel bad." In this case, you're describing yourself, so you use the adjective.
Does that make sense?