A stoppage-time goal from Alvaro Morata sealed Chelsea’s place in the last four of the League Cup where they will take on their London rivals.
Arsenal have got the better of Chelsea in the last three matches between the two sides, including victories in the FA Cup final and Community Shield.
It marks a shift from previous years when Chelsea dominated the head-to-head with six consecutive league wins between 2012 and 2014.
Arsenal and Chelsea will play each other three times in January, with a league game followed by the two-legged semi-final.
But while Cahill gives credit to Arsenal for their recent wins, he insisted Chelsea will be extra motivated to get a result.
“No, not at all. I have had good and bad times against them,” he told the Evening Standard.
“They’ve done very well against us lately, especially at Wembley but if I put myself in the Arsenal camp, I don’t think it’s ideal for them to play us over two legs.
“Do the recent results against them give us extra motivation? Yes. Obviously there was the FA Cup final last season and they got one over us there.
“But if you look at what’s happened over the last 10-15 matches between us, we have had good games too.
“We have played Arsenal many times and we know what to expect. The first leg is at home and that will be massively important. These are two big teams going at it.
“We know it will be a tough test. You expect to see big teams in the semi-finals of cup competitions, even though clubs change their sides up.
“You still expect the big teams to have enough to get through and that’s what’s happened with our semi-final.”