You and your baby will be fine! If you like, you could try some of these tips (edited - sorry it's still long!) from Eva Lyford for 'paced bottle feeding' which apparently helps babies feed more 'naturally' (if that's the word):
"This information is particularly targeted towards infants under 6 months of age. Babies should be bottle-fed:
When their cues indicate hunger, rather than on a schedule.
Held in an upright position; it is especially important to avoid letting the baby drink from a bottle when lying down. Such a position is associated with bottle caries and an increased frequency of ear infections. Note also that babies should be held often at times when they are not being fed, to avoid the baby being trained to eat in order to be held.
With a switch from one side to the other side midway through a feed; this provides for eye stimulation and development.
Care providers should be encouraged to make appropriate quantities last the average length of a feeding, rather than trying to feed as much as they can in as short a time as possible. This time element is significant because the infant’s system needs time to recognize satiety, long before the stomach has a chance to get over-filled.
Gently, allowing the infant to draw nipple into mouth rather than pushing the nipple into the infant’s mouth, so that baby controls when the feed begins.
Stroke baby’s lips from top to bottom with the nipple to illicit a rooting response of a wide open mouth, and then allow the baby to “accept” the nipple rather than poking it in.
Consistent with a breastfed rhythm; the caregiver should encourage frequent pauses while the baby drinks from the bottle to mimic the breastfeeding mother’s let-down patterns. This discourages the baby from guzzling the bottle.
To satiation, so that baby is not aggressively encouraged to finish the last bit of milk in the bottle by such measures as forcing the nipple into the mouth, massaging the infant’s jaw or throat, or rattling the nipple around in the infant’s mouth. If baby is drowsing off and releasing the bottle nipple before the bottle is empty that means baby is done; don’t reawaken the baby to “finish.”
The benefits of bottle-feeding in this manner:
The infant will consume a volume appropriate to their size and age, rather than over- or under-eating.
This can minimize colic-like symptoms in the baby whose stomach is distended or over-fed."
Even if this doesn't happen exactly like this at every single feed - heaven knows no two breastfeeds are the same - it can be helpful to use these tips that follow biological norms.
Though in my view, the most important thing is skin-to-skin contact and holding a newborn - research consistently shows it's good for brain development (see e.g. www.ncbi.nlm.nih.gov/pubmed/12647930 - most of the studies deal with pre-term babies but it's not like there's no benefit for full term ones, it's just less likely to be studied - mechanisms are the same).