Antibiotics kill off the good gut bacteria as well as the bad illness causing bacteria. It can help to give a probiotic (an hour after an antibiotic dose) as it can help them feel a bit better. Better still, use poop soup made from the incredibly fresh poops of a healthy companion.
As siikibam has suggested, perhaps try his normal pellets mushed with water either on their own or mix some of it into the critical care as it will familiarise the taste. Alternatively you could try a different type of recovery feed if one is available to you.
Switch to weighing him daily while he is unwell so you can monitor his food intake much more closely. if you are unable to get him to eat, then yes, do go back to the vet for help.
Just to clarify, should it be 0.6ml per day, not 0.06ml?
Probiotics, Recovery Foods And Vitamin C: Overview With Product Links