How regularly are you feeding? What kind of schedule are you on?
Babies get faster as they get older and more efficient - it doesn't necessarily mean less milk. When you squeeze your breast you aren't stimulating it in the way a baby does (unless you are 'hand expressing' which takes a bit of experience.) A normal squeeze from you doesn't reproduce what he does at the breast. It is more than likely he is still getting something out when you are not. Even if it is just a small trickle, it will be something. The breast doesn't really go completely 'dry' for the baby as the body continues to manufacture milk during a feed.
The best way to increase supply is to give him more time at the breast. Even if he is bobbing on and off I would keep him at the same breast a bit longer. When your baby 'has a growth spurt' it means he is feeding more to increase your supply in preparation for his increased needs. The way to respond to it is to avoid supplementation and focus on nursing time. Have a look at some of the other recent posts about low supply. There are lots of suggestions there including definitely making sure you are drinking enough yourself as mentioned by jacobmarksmummy.