Miller signed from Celtic for £3million, after he slipped down the SPL champions' pecking order, and penned a three-year contract at Pride Park.
"I'm choking to get a game. I'm desperate to get back fit and get back playing again," Miller lamented.
"It's very frustrating, I hate being injured, any professional would say the same thing. I am getting there now at least."
The Rams are currently rooted to the bottom of the Premier League, and have yet to record a victory, but Miller is confident his new side can turn things around.
"It's not great to be down there (at the bottom). I have chosen to come here despite that," he added.
"I have watched the Premier League and I see the players that are there and I believe Derby have a squad and have a good enough manager to stay in this league.
"The manager played a great part in me deciding to come. I think he has done a fantastic job in getting Derby back where they belong in the Premier League and hopefully I can still play a part in helping us stay there."