The Australia midfielder, 27, made his first senior appearance in almost seven months in Thursday's 3-1 victory against Greek outfit Larissa.
"Europe is very important to us because it is probably the thing that we've been missing," said Cahill, who signed a new five-year deal in the summer.
"We've done well in the league in the last few seasons but doing well in Europe is what the fans and players like myself have been waiting for.
"I've always wanted to play in Europe and this is a massive boost for myself and the reason why I re-signed.
"This is possibly the next level for this football club.
"We're pretty much established in the Premier League and the next level was to get to Europe and to try to make this pinnacle and a stepping stone to even greater things."
The Australian international continued," The team performance against Larissa was great and I was made up to get a goal."
"Overall, I'm just happy to get the minutes on the pitch.
"It's been very difficult but when you work with good staff it makes it easier and I could see the light at the end of the tunnel.
"It was a bit of a shock that I started the game but I'm just happy to be a part of us doing well in Europe.
"I've done all I can to get myself fully fit and now it's about playing games of football now."