"It's a really big game for us, one we hope to win and obviously put in a really good performance as well," said Republic of Ireland midfielder Miller, who moved to Edinburgh in September.
"We want to get back to winning ways as quickly as we can and we're obviously disappointed with the last game and looking to put things right."
The 28-year-old added: "The derby games are always special, with the bragging rights of the city.
"But it's going to be a really tough game. Hearts have been doing well quite recently and it's one we need to play our best to win."
Victory on Sunday would maintain Hibs' push for a Europa League spot.
European football is something for Miller to look forward to after he was denied the chance to play in this summer's World Cup.
Thierry Henry's infamous handball in France's play-off with Ireland still rankles with many but Miller is determined to move on.
Asked if he had been able to forgive Henry for his actions, Miller said: "You just wonder what you'd have done if you were in his shoes I suppose."
Hearts boss Csaba Laszlo has taken heart from the way Hibs' previously impressive defence was cut open by Rangers.
"Just the inspiration that even at Easter Road you can score four goals gives for us the possibility to see that we can," he said.
"If we score just one and don't lose any, I am happy."
Nevertheless, Laszlo has been impressed by the way John Hughes has transformed the fortunes of Hibs since moving from Falkirk in the summer.
He said: "He had a not so good season with Falkirk but now with Hibs it is a new team, new people around you, new players, different players and also the players who came into the club brought a lot of new and fresh air and also quality.
"And if you have the quality, definitely you have also success."
One of those quality players is top scorer Anthony Stokes, who Hearts tried to sign last summer.
Laszlo revealed he was "very close" to landing the Republic of Ireland striker as he kept his fingers crossed about acquiring another forward this month.
The Hearts boss has been trying to bring Izale McLeod and Steven MacLean to Tynecastle on loan this week.
Deals for the pair hang in the balance, with Vladmir Romanov quoted as saying he had yet to be convinced by them.