The Italian has made it clear that the Bianconeri were always optimistic about their chances of making it to the round of 16, despite the threat Chelsea and Shakhtar Donetsk posed
The Serie A champions struggled in their opening three Group E games, but eventually qualified for the round of 16 as group winners following their 1-0 away win over Shakhtar Donetsk on Wednesday evening, much to the delight of Chiellini.
"We knew it would be very difficult for us after the draw in Denmark, but we always believed we could qualify but only if we play like Juventus can," the 28-year-old told Uefa.com.
"On Wednesday, we played very well against a Shakhtar side that have a number of good players. We did what we had to do, we created a number of good chances to get the win and I think we deserved the victory.
"If you play for the draw you are likely to lose because Shakhtar have a number of great players that can hurt you.
"We tried to attack and we tried to win and we are really happy to go through to the next round of the Champions League."
Juventus resume Serie A action on Sunday when they travel to Palermo.