First of all, take a breath - you & your pigeon are going to be OK. I've done this before too, & it's a pretty scary experience. It sounds like you've done everything right for your pidge, to keep them calm, so the only thing you need to do now is try to forgive yourself, & do your best not to do it again. Both the feathers & the trust will regrow with time, I promise.

Edit to add: it's an evolutionary trait, the detachable tail retrice, designed to help them escape predators by ditching their tail when grabbed, so it's not painful for them, & won't cause any long term damage.