Waghorn and Tavernier, key performers as Rangers cruised to the Championship title last season, have rejected new contract offers.
Both players have two years remaining on the initial deals they struck when they joined Rangers 12 months ago but are believed to be unhappy with terms for extended deals.
Veteran striker Miller, who twice left Rangers during his career, has defended the right of Waghorn and Tavernier to seek improved terms.
But he also believes both players must build on their initial impact for Mark Warburton’s team by proving they can be equally effective in the top flight of Scottish football.
“I would say the grass is not greener elsewhere,” said Miller. “These things happen in football when it comes to contract negotiations. Waggy and Tav were great for us last year. It’s always hard to hit the ground running at a new club, especially when it’s a club the size of Rangers.
“Wes Foderingham, Rob Kiernan, Andy Halliday and Jason Holt too were outstanding through the season – as were Waggy and Tav. They had good seasons. We’ve got to be real about it. It was at a level this club is not used to playing at. It’s about this season and turning up and putting in that same level of performance as last season.
“Knowing the lads, how they talk about this place and how they go about their business on a daily basis, they fully appreciate where they are. They know the size of the club and the expectation levels that are on them here, week in, week out.
“Those expectations will be even more this season. The demands will rise as will the challenge. But the lads are fully aware of that. These things are part and parcel of football when it comes to renewing contracts or transfers. It’s never plain sailing.”
Miller continued: “I think they really enjoy where they are. There are a lot of factors coming into play when it comes to signing a new deal.”
Waghorn was Rangers’ top scorer with 28 goals last season, despite sitting out most of the end of the campaign with an injury. “There’s no doubt we missed him when he was out,” added Miller. “To lose him – and the number of goals he scored – and to kick on and put in some fantastic performances without him was great. But he is big player for us and a real goal threat from wide or through the middle. He is eager to do even better this season.”
l Miller was speaking at Ibrox as Rangers players and coaching staff teamed up with Callaway golf tour professionals for a one-hole Par 3 challenge and penalty shoot-out on the pitch ahead of this week’s Open at Royal Troon.