The Blues had dropped their past three matches - in the UEFA Super Cup, Premier League and Champions League - before they beat Fulham 2-0 at Stamford Bridge and defender Cahill felt it was a nice way to answer the critics.
"Two dodgy results back to back got everyone talking," Cahill told the club's official website.
"When you are a big team and you lose two games it gets talked about as a crisis. It was not ideal but we didn't feel that way.
"We looked a bit tentative first half but the second half we created a lot more chances, put Fulham on the back foot and we looked a better side.
"It was much more like us and that is why we got our joy.
"The second half was how we should be playing at home. It takes time when new players come in but we have a great squad now, a proven manager and I am sure we will do well.
"At the start of the season I thought we were playing some great stuff but it does take time because we have players needing to adapt to the league and to adapt to being here."