Cahill feels belief is rising in the camp as the fixtures keep coming thick and fast.
"It was a day when everything came together for us," the defender told chelseafc.com.
"We started the game really well which set the tempo. We were good defensively and going forward we were brilliant and created a lot of chances. There were plenty of goals and plenty of goalscorers.
"Without being disrespectful to Aston Villa, it is a rare scoreline and you feel a bit sorry for them but at the same time, we had to do a job and we have shown what we can do.
"The positive thing was we didn't sit back when we had scored two or three. We kept going until the 90th minute and we got our rewards for that and that will give us confidence leading in to the Norwich game."