Josh Walker equalised for the Millers, but a late goal by Accrington's Ryan meant Stanley emerged with the win.
"We stood up and were counted against a good side and back-to-back wins is what we needed after a mini-slump," said Coleman.
"We played some fantastic football at times and we deserved the win. We showed a great enthusiasm and willingness to work hard and we scored two great goals.
"The run-in for me starts in August and we have just got to keep getting as many points as possible."