The former Wolves striker followed up his spectacular winner against Newcastle by scoring for the Rams during Saturday's 1-1 draw with fellow strugglers Bolton at Pride Park.
Miller, who netted three times for the Bhoys before moving to Derby, told the club's website: "I still don't feel like I'm 100% fit and I'm getting a bit tired towards the end of games.
"But it's been a good start and on another day it probably could have been two or three goals for me against Bolton.
"I did well in the early part of the season at Celtic and as a striker you're judged on goals.
"This time last year I was sitting without a goal at Celtic so it was good to get three in the bag for them and now another two for Derby. That's always what you want as a striker."
The Rams have picked up four points from Miller's first three games and he believes home form will be crucial if they are to stay in the top flight.
The 27-year-old said: "If you're getting beat at home then it's always an uphill struggle.
"We beat Newcastle, who are a top Premier League team, and then we've drawn with Bolton and were unfortunate not to beat them.
"It might well be a very good point. We'll find out over the next few weeks."