The Turin giants lost 1-0 to Galatasaray in their vital Champions League clash on Wednesday, ensuring they will drop into the Europa League for the remainder of the season.
Although both Antonio Conte and Roberto Mancini felt the playing conditions were dangerous following the snowstorm in Istanbul on Tuesday evening, Chiellini insists his side were made to pay for their poor results earlier in the group stage.
"It was a 0-0 game and it remains bitter in our mouths because we could've come into this match already qualified," he told reporters.
"I have regrets because we compromised our qualification in the first two games of the round. The two main mistakes were the games at Copenhagen and the one at home against Galatasaray where we threw away the win.
"We could not achieve our goal of qualifying for the round of 16 and we are sorry because today you couldn't play football on an impractical field.
"Yesterday when it was possible to play football we didn't concede anything to Galatasaray, but today we couldn't do the same. It was straightforward until the 85th minute where we suffered from the goal that eliminated us."
The 29-year-old was also quick to defend the Europa League, insisting his side will fully respect the competition, the final for which will be played at Juventus Stadium.
"In terms of the Europa League, we must be motivated to win it: like Chelsea did last year when they were eliminated (from the Champions League) then went on to win the Europa League," he continued.
"It's too early to talk about the final in Turin because there is a lot to play for in Serie A and Coppa Italia. We will treat the Europa League with the right mentality and the right concentration."