The 26-year-old praised his team-mates as Chelsea kept their second clean sheet and win in a row under caretaker boss Roberto Di Matteo.
Cahill is looking forward to forging a partnership with the former England skipper following his absence through injury.
He told the club's official website: 'It felt solid and I think defensively as a whole we all played our part. Branislav Ivanovic played fantastically in the first half and then David Luiz has come on and done well. Having John back is obviously a positive for us, and we defended really well and deserved our clean sheet.
“He's got massive experience and we were solid. I had a little relationship with England with him and this was the first Chelsea game I played alongside him. I think it works well but we all had a part to play and contributed. As a unit we looked a lot more solid.”
The former Bolton defender has revealed the players have carried on as usual following the sacking of Andre Villas-Boas and feels Di Matteo is having a good effect on the team so far.
“It's been good, the response to him has been positive and we've had two good results," he said. "It has been strange. I feel I am settling down now and feeling a part of the team, I hope it shows on the pitch.
“The new manager has put his spin on things, just the way he does his training sessions are a little different, but the personnel around the place has not changed too much. It's been positive, and the lads have responded positively to it.
“We're getting on with the job we have to do, it's not nice when the manager loses his job, it was a sad moment for everyone, but it's a cruel game and you have to move on.”
Cahill revealed he was disappointed with his performance on his Champions League debut against Napoli, as the Blues succumbed to a 3-1 defeat. The England international is hopeful the team can bounce back and have a successful end to the season.
He added: “Conceding goals is not a nice feeling and on the night everything went wrong that could have done so it wasn't a pleasant Champions League debut and hopefully we can put that right.
“Defensively we were poor and I was a big part of that, Saturday was miles better and we're getting more of a relationship and solidarity, like at Birmingham. Hopefully we've turned the corner and results have gone well in the last couple of games.
“This is an important week for us and we have two more massive games now to contend with [with Leicester to follow in the FA Cup], but with a couple of wins we have confidence and know what we have to do on Wednesday.”
Want to be at the Euro 2012 opener? Who doesn't? With Sharp FanLabs you can win free tickets to the opening event of 2012's biggest tournament. Click here to take part!