Managerless County dominated the game for long periods, with the Millers having Nick Fenton sent off for two bookable offences in the second period.
"The first-half performance from us was totally inept," said Moore.
"Every time we regained possession we gave it away and I thought we were very fortunate to come in at half time 0-0.
"We changed things at the break and went with three up front, but we couldn't really get that going because Nick Fenton got sent off.
"But we cannot play the way we did in the first half, we cannot give people the 45 minutes start we gave them.
"Yet after the sending off we dug in deep and Andy Warrington made some good saves, but we were playing at home and we should do better than that."