Tiny bruises can occur after microneedling but they clear in a few days. If you have actual veins, they can be treated with IPL or a vascular laser.
If you truly have broken capillaries as a result of microneedling they will not go away on their own. Intense pulse light (IPL) treatments are often highly effective in treating these sorts of lesions. You may need multiple treatments. I recommend scheduling a consultation with an experienced provider in your area.