Success at Eastlands saw the Toffees deny City the opportunity to top the Premier League table at Christmas, while giving themselves a welcome shot in the arm.
Three hard-fought points lifted
Everton
into 14th place, with just six points now separating them from Tottenham in fifth.
There is still work to be done if a slow start to the campaign is to be countered, but the outlook is looking a lot brighter.
Cahill, who broke the deadlock against City, believes that to be the case and the Australia international is of the opinion that Everton's luck is starting to turn.
"The achievement is massive for us," he told.
"We knew we had to work hard, but what's been going on in the last couple of months, we've been working, playing some good football and not got the rewards.
"But we've come to a stadium where it is hard to play and showed our mettle and played some good football too."
Cahill was also quick to praise goalkeeper Tim Howard after the City showing, with the American having pulled off a string of smart saves to keep Roberto Mancini's side at bay.
"He's been the man not just this season but all the other seasons as well. It's what he brings to the team," he said.
"There's times in games when we look to him to get us out of it and he did that."
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