The London 2012 heptathlon champion's coach Toni Minichiello said the decision to close the close the stadium could cause the death of athletics in Ennis's home city of Sheffield.
The Labour-run council said it could no longer afford to keep the facility open as it tries to cut £50 million from the local authority's budget.
"I'm gutted and pretty angry to be honest," Minichiello told the BBC.
"Athletics is pretty close to being dead in Sheffield because of this decision.
"We're going to be all right for this coming season because it's open, but any sort of move towards the next Olympic games and retaining Jess's title has been dealt a hefty, hefty blow."
But Minichiello said it would damage not only Ennis but young athletes inspired by the success of London 2012.
"They have got no future because when Jess started she had the Don Valley stadium where, yes, we could train outdoors but there was also a smaller indoor area which we could use that made us fairly weatherproof."
Councillor Bryan Lodge said: "It is with a very heavy heart that we have arrived at this decision, but we are having to take out £50m from our budget for the next year on top of what has already been saved and it isn't getting any easier."
The council said it would spend £700,000 on the stadium this financial year, equating to more than £5 per visit.