Thomson became the latest player to quit the Scottish champions this summer, when he signed for Middlesbrough in a £2million deal.
He joins former Ibrox team-mate Kris Boyd at the Riverside, just weeks after the striker's own departure from the Scottish champions.
Miller said: "Losing Thommo is a blow. He has been a regular starter for the team over the last two or three years he has been at the club so he will be a loss.
"But you've got to move on. When one door closes, another opens. There are lads who are more than capable of filling his shoes.
"Lee McCulloch, Steven Davis, John Fleck and Maurice Edu can all play in that position. We have more than cover for him. It's an opportunity for somebody else to come into the team."
As well as Thomson and Boyd, Nacho Novo, DaMarcus Beasley and Steven Smith have also left the Scottish champions since the end of last season.
So far, attempts to add to the squad have failed after Burnley winger Chris Eagles rejected a move to Rangers after failing to agree personal terms.
Miller added: "The manager has a job to do and if he is going to bring a few faces in, that will happen over the course of the transfer window.
"As players, we've just got to focus on getting fit and looking forward to the upcoming games in Australia and against Newcastle before the season starts."
Miller admits new personnel is vital but was also keen to point out that Rangers have been able to cope without an injection of fresh talent for the last two years.
"If we don't sign players, we will have to be good enough," he said, as he modelled Rangers' new away kit.
"But we are looking at hopefully bringing in a few fresh faces. We have lost a lot of players.
"With Thommo gone, that's five important first-team squad players so we are going to have to replace at least a couple of them, I would think.
"But, if nobody comes in, nobody comes in. It's something we have had to deal with for the last couple of years.
"We hadn't brought anybody in but we hadn't really lost any big players, like we have done this summer.
"But if nobody comes in, we will carry on regardless as we have done for the last couple of years and hopefully retain our title."
Like Thomson, Miller has a year left on his current deal but says he has no plans at the moment to join the exodus.
He said: "At the moment, I've not had any decisions to make. I'm in the last year of my contract and we will wait and see what happens."
Asked about a new deal at Rangers, he added: "If the option was there, I would definitely listen to it."