Chelsea capitalised on second-placed Tottenham Hotspur's 1-0 defeat by West Ham United on Friday by beating Middlesbrough 3-0 on Monday to move seven points clear at the top with three games left.
Three more points would put Chelsea out of reach of Tottenham, who face sixth-placed Manchester United on Sunday.
"It's one more to go, we have two home games and one away so we're in a very good position now," Cahill told the club's website (www.chelseafc.com).
"If anything we should be enjoying it. After the Tottenham result (against West Ham), naturally spirits were high in training and everybody was buzzing..."
Cahill said that Chelsea are keeping their concentration and are hopeful of getting a win at the Hawthorns, where they have won just once in their last five league visits.
"The pressure is still on because we have to win one game out of the three, but with the way we're playing there's no reason why we shouldn't be confident. We're still doing the right things, there's no complacency," Cahill said.
"It's going to be a tough game at West Brom, it always is. It's never comfortable and we need to be aware of that, but we're looking forward to getting the job done."
Chelsea could draw from their experience in the successful 2015 title race, Cahill said.
"It was probably more comfortable last time but the run-in is always the same, there is always a stage in the season when it's going to be tight, when teams are putting pressure on and you're having to win," he said.
"That's helped us this time, having the experience of that. We're in a great position now and if we were to throw it away we'd be devastated."
Chelsea host Watford and already-relegated Sunderland in their final two games before the FA Cup final against Arsenal on May 27.
