a lot of mom's don't burp their breastfed babies at all. I only will wake her up to burp her if I still have to change her diaper or I'd she's been spitting up that day other wise I let her sleep

As long as he doesn't wake up fussy it should be okay. I don't burp my daughter after her feed that she falls asleep on. I usually nurse on one side, burp, and then nurse on the other which she really just sucks to fall back asleep. Lol