Giteau starred for the Wallabies in the 49-0 drubbing of South Africa in Brisbane three weeks ago with two tries in what was his first appearance in the 'green and gold' this year because of injury.
However, Giteau has been barely noticeable in the two Tests against New Zealand and the Springboks since, and Ella believes Connolly is not making the most of the 23-year-old.
"It's stupid to have the six million dollar man in the team and not use him," said Ella, who won 25 caps for the Wallabies.
"He's under-utilised, but you could say that about half a dozen of the Australian backs. He is one of the best attacking inside centres in the game, but we neutralised him."
Giteau was used as a decoy in the 13-9 loss to New Zealand, and in the recent 20-18 win over the Springboks, he again found himself out of the action as the Wallabies relied on Stirling Mortlock as first receiver.
"The Springboks targeted Stephen Larkham, but playing Mortlock at first receiver negated the interaction between Larkham and Giteau," Ella said.
"Larkham and Giteau should be involved in the play. They shouldn't be running plays to shield them. If they are not up to it, find someone else."
Meanwhile, Australian forwards coach Michael Foley has refused to single out second rower Nathan Sharpe for criticism following the Wallabies' poor line-out efforts in the win over South Africa.
"We lost four line-outs and the quality of our ball was not good," Foley said.
"We don't want to blame Sharpe for our line-out. We have to take shared responsibility, myself included."
Foley also came to the defence of hooker Tai McIsaac - who played ahead of Jeremy Paul - for his throwing in the game.
"That was a long way off Tai's best throwing," Foley admitted. "But he is an outstanding thrower. He's as good as anyone.
"He was under pressure he is not used to. It was a new experience for him. It's only his third Test. He was up against the best defensive line-out in the world in Victor Matfield and he had a difficult night at the office.
"But I still have faith in Tai and he will be better for the experience."