Iceland were within two minutes of claiming a win that would have all-but secured their place in the last 16 of Euro 2016 when the unfortunate Birkir Saevarsson diverted Nemanja Nikolic's low cross into his own net.
Sigthorsson, who was named man of the match for a robust display in attack, revealed the Iceland dressing room was flat afterwards.
"We were five minutes away, we just failed to finish the game off," the Nantes striker said.
"We were winning a lot of second balls but we should have kept calm and played the ball more. When we got the ball we weren't calm enough.
"It was obvious, today we wanted to go for the three points. We were so close, the guys are so disappointed in the dressing room."
Sigthorsson added: "We were close to sealing it this time but hopefully we can go into the last game and take all three points.
"We are a strong side with some good characters and we will try to get three points against Austria.
"It feels like a loss, that’s all I can say, but we are still unbeaten so we can still be positive.
"We go with full confidence into the last game, it will be a big match and hopefully we get the three points and go through."