Cahill said the Blues' squad had as much confidence in their manager now as when he masterminded their march to Champions League glory exactly six months ago today.
That earned caretaker Di Matteo a permanent contract but he goes into Tuesday's Group E game at Juventus under real pressure after an alarming slump in form, which has seen them lose three of their last seven matches.
"We're all behind him and he's definitely the right man," Cahill said. "He proved it last year and I'm sure he will prove it this year as well."
Saturday's Barclays Premier League defeat at the Hawthorns -- which left them with just two points from the last 12 -- was said to have prompted a furious row in the dressing room between players, with Di Matteo also thought to have read them the riot act.
"In the short space of time I've been here, losing games is not acceptable. When you do lose, people are disappointed, hurt and upset," Cahill said.
"Sometimes, things need to be said and I think it's great to have that reaction," he added. "I'd be worried if people were just going in, getting showered and then getting on the bus. What happens in the changing room stays there, but it's definitely a positive reaction when that happens in football."