The Australian praised his team-mates' performances at the Stadium of Light and highlighted their resilience as the Toffees booked a semi-final meeting with Liverpool
The Toffees produced an excellent display at the Stadium of Light and booked a semi-final tie against Liverpool thanks to a Nikica Jelavic strike and an own-goal from David Vaughan.
They will now face bitter rivals Liverpool at Wembley, and Cahill was understandably proud of the team's effort.
"We showed great spirit tonight. We have a disciplined squad with a great attitude," he told ITV.
"The manager knows what we are capable of and it is about time we started producing performances like this."
Everton created and missed a host of opportunities in the second-half, with Jelavic the main culprit, but Cahill insisted the Croatian has brought a lot to the squad.
He continued: "Listen, he's been brilliant since he came here. He has changed a lot of our games. The way he holds up the ball is excellent and he brings others into play.
"It doesn't matter if he misses. He scored tonight and we all work hard for each other anyway. We have each other's backs here."
Everton face West Brom at Goodison in their next game and will be looking to keep their form going as they hope to overcome rivals Liverpool in the FA Cup and the English Premier League.