Italy scored twice in extra time through substitutes Federico Chiesa and Matteo Pessina to give the Euro 2020 title contenders a nerve-racking 2-1 victory over Austria on Saturday and a spot in the quarterfinals.
The Azzurri, who are now unbeaten for 31 consecutive matches -- a new national record -- got off to a strong start and hit the upright with Ciro Immobile's powerful shot in the 32nd minute.
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But Austria, looking for their first win over Italy in 62 years, grew bolder after the break and put the ball in the net through Marko Arnautovic, only for his 65th-minute header to be ruled offside after a VAR review.
They ran out of steam, however, early in extra time allowing Chiesa far too much time and space in the 95th to control a Leonardo Spinazzola cross in the box and rifle home from a tight angle.
Pessina also found enough space to drill in from close range in the 105th before Sasa Kalajdzic pulled one back for Austria with a glancing header.
"We knew there would be some potential banana skins in this match and we thought it might even be tougher than the quarterfinal," Mancini told a news conference.
"Of course, Austria are not as good as the teams we will face in the next round, but they really make life tough for you. We watched a lot of their matches and they do cause problems.
"We knew that if we scored in the first half it would have been a different game. We didn't manage to and so we had to dig deep. The players really wanted to win at all costs."
Austria coach Franco Foda told reporters: "We wanted to write history and we succeeded. It was an important learning process for us.
"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 quarterfinals against one of the title favourites.
"Even after 2-0 behind the team kept believing. That was very impressive. We had a good dynamic. Defensively we were very solid."
Italy will now play either Belgium or Portugal in their quarterfinal next Friday in Munich.
Mancini would not be drawn into saying which player he would rather avoid in the next round.
"When you get into the quarterfinals, it is not that easy. Ideally we would like to avoid both, but that is not possible," he said.