You do not, in fact, pay for better service with Comfort+. It's still coach with regular coach service. More legroom and free drinks and a slightly less meager snack but it's still coach. It is not a cabin with a dedicated staff. DL's comparison of the different fares specifically mentions "attentive service" as a benefit of F, but not C+. Therefore you don't get to interrupt the ongoing service further back to get a drink refill. When they come around again you can ask then, or you can get up and walk to the galley and ask. If you need more attentive service, pay for first class.

FA could certainly have delivered this message more diplomatically. I attribute that at least in part to a lack of training.