Glasgow saw off Edinburgh 33-14 in the URC match, played at the home of Scottish football for the first time, over the weekend and the sides meet again on 28 December for the second leg.
"We stuck to our processes in the first half especially and the start of the second half," Miller told glasgowwarriors.org.
"Being at a new stadium, here at Hampden was really fun.
"To have so many fans out here and coming out to watch and support the game is great.
"We have been working on our away processes for the last few seasons. We will see it as another week, its always good fun going away from home now."
"Back up the good parts of today's performance and, as every week, you don't need to lose to get better."