While antioxidants are found within many whole food sources, it's very important as a vegan to ensure you're supplementing the core nutrients that your body is otherwise unable to generate itself or source on a vegan diet.
For example, antioxidants can be found in sources of vegan products fortified with B12, but without supplementing B12 (an essential vitamin to combat neurologic problems and blood diseases), you may well have suboptimal levels, as fortified foods provide irregular levels of B12. The same applies to Omega-3 for vegans.
Here is a snippet from Harvard Health Publishing:
"There are no known plant foods that are natural sources of B12. Fortunately, eating fortified foods, such as breakfast cereals, soy milk, and vegetarian meat substitutes, can help prevent a potential deficit. However, research shows that vegans who don't take a B12 supplement often have inadequate B12 levels."