Chelsea face Qarabag in their opening group tie this week.
Cahill said: “We’re back where we deserve to be on the basis of our consistency over the majority of the seasons since I have been there.
“Obviously it’s an enjoyable competition to take part in and all the best players — ourselves, the Brazilians, the Spanish players — everyone wants to be in that competition, that’s what attracts players to come to clubs.
“People want to be playing at the top of their game, like Monday in international football.
“So for big players it’s important you’re in the competition and we’ll try to go as far as we possibly can in it.”