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."

11 May 2014 Last updated at 11:24 BST
Hundreds of volunteer builders gathered in the city centre to make the tower, using 1,000 cardboard bricks.
The People's Tower community art event was created to mark the opening weekend of the annual Norfolk and Norwich Festival.
The tower is 22 metres tall and is designed to look like the St Peter Mancroft Church tower.
It took more than eight hours to complete and was held together by more than eight miles of packing tape.
It was designed by French artist Olivier GrossetÃªte.

The woman, 39, suffered "multiple serious injuries" after plummeting to the ground during a "routine" jump over Salisbury Plain, Wiltshire, on 5 April.
Police said it was miraculous she had survived, after her main chute failed and a reserve only partially opened.
A 35-year-old man was arrested but has since been bailed, police said.
Wiltshire Police began an investigation after being alerted by the parachute club at Netheravon Airfield to concerns over what had happened.
Detectives said they were particularly looking for "slinks" or soft links, used to connect the canopy to the parachute harness, which were "missing".
Det Insp Paul Franklin, said the woman, an experienced parachutist, had "very nearly lost her life".
"This woman would have been dead if her chute hadn't partially opened, this meant her descent was slowed enough for her to survive the fall," he said.
The woman was taken to Southampton General Hospital with "multiple fractures throughout her body" and was now recovering at home, police said.
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.
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A church made of cardboard boxes has been built in Norwich.
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A man has been arrested on suspicion of attempted murder after a woman's main parachute failed to open in a 4000ft (1,219m) jump.