The Premier League outfit fell at the semi-final hurdle following a 3-1 defeat to Atletico at Stamford Bridge on Wednesday night.
"We're heartbroken," Cahill told Sky Sports News. "One game to the final and we couldn't quite manage it - we're devastated.
"We started off really well but they got back into the game. We tried to create, the effort was there, but we just fell short. They're a good side. They caused us a few problems and their keeper produced a fantastic game.
"We have to be over it by the weekend. At the moment it's raw and it will take some getting over but we'll see what happens in the next few days."
Chelsea, who will play Norwich City at home this weekend, remain in the Premier League title race as they currently reside two points behind leaders Liverpool in the table.