Austria kept believing it could come back from two goals down against Italy in extra time in their last 16 game on Saturday but ultimately paid the price for small mistakes, said coach Franco Foda.

Italy had to wait until extra time to score two goals to beat the Austrians 2-1 and book their quarterfinal spot. But even after conceding twice, the Austrians battled back to cut the deficit and missed chances to level.

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"We wanted to write history and we succeeded. It was an important learning process for us," Foda told reporters.

His team was victorious in two group matches, its first ever wins at a European Championship, and also advanced to the knockout stage of the tournament for the first time.

"We are all disappointed by the elimination but we can all be proud of our performance over 120 minutes. We wrote history, reached the round of 16 and were close to reaching the quarter-finals against one of the title favourites," Foda said.

"Even after 2-0 behind the team kept believing. That was very impressive. We had a good dynamic. Defensively we were very solid," he added.

The Italians, who had won all their group matches and are now unbeaten in 31 matches, broke the deadlock with goals from substitutes Federico Chiesa and Matteo Pessina.

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"After 90 minutes we were convinced they had felt we were causing them major problems. Our belief was huge but teams of Italy's quality will use their chances and then you are suddenly behind," the coach added.

Chiesa was left with far too much space as he fired Italy ahead while Pessina was marked too late when he rifled in the side's second goal. "But that's football. Goals are scored through mistakes. But we kept believing at 2-0, we scored and then had a couple of chances. It is bitter that we did not score an equaliser. It would have been deserved over 120 minutes," Foda said.

Sasa Kalajdzic scored in the 114th minute for Austria but despite piling on the pressure, it could not find an equaliser.

"Austria can be proud of they way they presented themselves. Now we want to pick up in September (with the 2022 World Cup qualifiers) where we left off here because we want to go to Qatar next year," said Foda.