The Blues came from behind on Monday to earn a 3-1 victory at Turf Moor in their opening match of the season.
"Obviously it wasn't ideal that we went 1-0 down, but the reaction from the lads was fantastic and we kind of put the game to bed in the first half," Cahill told the club's official website.
"It was a sticky scoreline because if they get one back it's game on, but in the second half we played very direct as we probably would have expected to.
"It was a tough game, which we knew it would be, but we're thrilled with the three points."
Chelsea return to action on Saturday when they host Leicester City in the Premier League.