Italy did not qualify for the 2018 World Cup, the first time they failed to reach soccer's global showpiece since 1958, and will miss Qatar after Aleksandar Trajkovski's last-gasp strike earned North Macedonia a famous win.
"I am proud of a team that has given everything, it is clear that we are destroyed and crushed, a great void will remain within us," said Chiellini, who replaced Gianluca Mancini in the 90th minute.
"There is a great disappointment, even today we played a good game but we couldn't score. From September to today we have made mistakes and we have paid for them."
Midfielder Marco Verratti said North Macedonia's goal in added time was a "real nightmare".
"This group had a great chance at the World Cup, we came from the unbeaten record, so it is difficult to accept what happened tonight," Verratti said.
"We all know that we have given everything, now surely it is time to ask ourselves some questions."
