The tournament has not exactly been at the top of the list of priorities for European clubs down the years, with the Champions League seen as the ultimate prize.
But Cahill revealed how spending four days in Japan - where the competition is treated very seriously indeed - had driven home how significant it would be to be crowned world champions.
"When I came to Chelsea, I came to win trophies," the England defender said.
"This is a big opportunity to do that. It's a fantastic competition and one that doesn't come around very often.
"It's hard to get into this competition in the first place.
"We've travelled all this way and we now want to win it.
"We've got some Brazilians in our squad and it's absolutely huge for them.
"It's sunk in how big it is, and we want to do well in it now."
Chelsea arrived in Yokohama on the back of two straight victories after interim manager Rafael Benitez failed to win any of his first three games in charge.
Cahill revealed the former Liverpool boss's ideas had begun to bear fruit.
"Defensively, as a team, we've tightened up which has given us a platform to build from," he said.
"It was hard for him to get all his points across at first because he was playing games every couple of days, but now the lads are fully aware of what strategy he's come up with and what's expected of them.
"It's working well at the minute."
All that will change if Chelsea suffer an embarrassing exit on Thursday and Cahill was taking nothing for granted against opponents who have already improved on last year's fifth-placed finish by winning their quarter-final.
"They're a good footballing team, get the ball down and play," he said.
"They also have the option to play long to the big striker, and can play off the second balls.
"They've got some talented footballers and had a good result in the last game, so it'll be a tough test.
"We'll be well aware of them come kick-off."
Monterrey have also had more time to adjust to the time difference.
Cahill said: "The jet-lag...
"It's been okay. When we first came it was strange for us.
"We all stayed up late and tend to wake up late. We've adapted in that way.
"We've had a few days, and personally I feel okay now. I feel fresh and ready to go."