Warriors sit second in the URC table but attention will turn to European action over the next couple of weeks. Racing 92 visit Scotstoun tomorrow before Glasgow travel to take on Harlequins next weekend eager to turn around last season's round-of-16 elimination at the same venue.
Back-row man Miller says that the squad would take each challenge as it came.
Speaking in the East Lothian Courier, Miller said: "Cliched as it is, we go one game at a time.
"We know the challenge ahead and we've just got to get our heads down and the hard work we put in every game, we're just going to show it on the European stage as well."
Miller returned from injury to start both legs of the 1872 Cup derby against Edinburgh and the former Preston Lodge and Musselburgh player was delighted to get the nod against the side he left to join Glasgow in 2021.
He said: "We've got a good squad at Scotstoun so, when you have an opportunity to get a run, you've got to take it with both hands.
"There's a lot of guys grafting away in the background.
"When you get an opportunity to put the shirt on, you have to go out and perform.
"I'm really proud of the efforts that everyone is putting in. But there's always more to come."
Warriors have had a strong first half of the season, with no signs of any post-URC title hangover.
Miller says head coach Franco Smith is constantly setting new targets for his players.
"Franco is really good at motivating us towards new goals, higher goals and keeping us motivated," he said.
"We're learning a lot as a team and using the whole squad effort as well over the last two weeks. So it's just going to build us into the end of the season and getting fresh bodies and peaking at the right time."
Speaking before the turn of the year, Miller said there would be no let-up in training, even though the players wouldn't be at Scotstoun.
He added: "We've got a few days off. We'll enjoy New Year.
"Family is a massive part of the club and Franco really values that aspect.
"So to get away and spend some time with the families and get away from Scotstoun will be good.
"We've still got our running and our gym sessions to tick off. Franco puts a lot of trust in us.
"He gives us the space and puts the trust in us to get the work done while we're away from Scotstoun as well."
Now, focus is firmly on Friday's crunch meeting with Racing 92.
"We'll throw everything we've got at them," said Miller.