Saturday's fixture - abandoned after 60 minutes amid torrential rain - will be replayed on 20 September, with no refunds offered for the original match.
Rovers boss Darrell Clarke called the move "shocking" and Swindon were urged to "rethink" by their Supporters Trust.
Rovers have offered returning away fans free coach travel to the County Ground.
"While we understand supporters' frustration, what happened on Saturday afternoon was an act of God and beyond the club's control," Power said in a statement on Swindon's website.
"I must stress that the club still has a number of costs to meet on a matchday. These costs have increased dramatically due to the fact that this is a derby match.
"Clubs do not usually offer any form of refund when the game is abandoned after half-time and not before."
Adult tickets for the rearranged match on 20 September will cost £19-25, although Swindon's season ticket holders will be admitted for free.
On Tuesday, Mike Welsh, vice-chair of Swindon Town's Supporters' Trust had told BBC Wiltshire: "Supporters were asked to keep their ticket stubs.
"We thought the club could have reached out to the fans and sought some middle ground. We encourage them to come back, have a rethink and see if we can meet the fans halfway."
Swindon Town chairman Lee Power is standing by his club's decision to charge fans for new tickets for a rearranged game against Bristol Rovers.