The Blues were dumped out of the semi-finals with a 3-1 second-leg defeat to Atletico Madrid at Stamford Bridge on Wednesday.
But they are still very much part of a gripping Premier League title race and Cahill says they must recover emotionally before a crucial home clash against Norwich on Sunday.
"We're heartbroken," he told Sky Sports. "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.
"But the timing of the goal was dreadful from our behalf and it was a sloppy goal to concede. We haven't conceded too many like that so it's disappointing.
"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."
The defeat was Jose Mourinho's sixth in Champions League semi-finals but they remain just two points behind Premier League-leaders Liverpool, with two games left.