The Toffees went down 2-1 in the semi-final after throwing away a one-goal lead in the 218th Merseyside derby.
Cahill said: "I think it's going to be difficult for them. They've had an indifferent season and they've just got away with it today.
"A few decisions didn't go our way but I'll just say they've got a lot of work to do."
Cahill had been hoping it would be third time lucky for him in the FA Cup, having been a runner-up in 2004 and 2009.
"This is sad because I've had two finals before in the FA Cup," he said. "And to now not get to a final, it's heartbreaking.
"But, as much as it is for me, I really feel for the fans because it was there - you could feel it and touch it - and even as players we didn't do it in the end."