The Australia midfielder is convinced the Merseysiders can still be a powerful force in the Barclays Premier League despite their financial problems.
Saturday's 2-2 draw with Aston Villa was preceded by a peaceful protest by several hundred supporters frustrated at a lack of investment under chairman Bill Kenwright.
Organisers carried a cake to Goodison Park to mark the second anniversary of the last significant transfer fees the club paid.
Yet lifelong fan Kenwright, who has long said he will sell the club if a suitable buyer emerges, remains popular with many other supporters and was applauded during the game when he appeared on the big screen.
Cahill found the atmosphere inside the stadium inspirational and feels the club will progress if everyone is fighting for the cause.
The 31-year-old said: "I think for us as players we want to try to show the fans that this isn't a club in stagnation.
"We need them to back us to the hilt. We know they do.
"The club are trying to balance the books and make sure we are here for years to come.
"We can understand their frustration, but the biggest thing for us is we want to make sure they feel this is still a strong squad.
"As an Evertonian, whether it is good times or bad times, you have got to roll with it.
"The protest when you look at it now was probably something that shouldn't have happened.
"But I know deep down they appreciate the chairman. They just feel there must be a change because they see every other club spending a lot of money.
"But he loves this club and loves the players. He has looked after us and treated us like his children, the manager the same.
"All we can do is fight for him and fight for the cause and make sure the fans know this is what we have to deal with."
Disquiet has been growing in some sections of support for some time but has noticeably increased since the deadline day sale of playmaker Mikel Arteta to Arsenal.
With Jermaine Beckford and Ayegbeni Yakubu also leaving, debt-hit Everton are thought to have brought in around £15million.
It remains to be seen whether Moyes will be given any money to strengthen in January of if those vital funds must be used to appease the bank.
Cahill said: "It is difficult for everyone but the reality is this is football, this is what we live in.
"If we had a couple of hundred million like they do across the park it would be a different story, but it is not.
"It is hard, Mikky was one of my closest friends and someone I admire a lot, but the whole scenario was right for everyone.
"Mikky might go on to play for his national team and he is going to play in the Champions League, which is something he wanted.
"It is also good for the club. He is off the books and raised a lot of money.
"We never want to lose a player like that that has given so much to the club but we want to make sure this club is alive for years to come."
Everton were at their dogged best yesterday, producing a fluid attacking display with Cahill and Leon Osman operating as makeshift strikers.
Osman fired them into a deserved half-time before Villa finally rallied after an insipid first-half display to level with a Stiliyan Petrov stunner.
Everton, finally winning a penalty after two previous appeals were declined, went back ahead with a Leighton Baines spot-kick but Gabriel Agbonlahor equalised late on.
Villa boss Alex McLeish, whose side remain unbeaten, said: "It's great to have made an unbeaten start and I'm much happier than I would have been after a defeat, but it would be nice to get a few victories on the board.
"We want to build on the confidence of the performances recently and this second-half performance.
"We never looked forward enough in the first half. Everything was square or back to Shay (Given).
"We never really got out of our half as Everton pressed us high but we changed it second half, went 4-4-2, and it was a terrific performance from Agbonlahor."