The tournament debutants came within two minutes of all-but securing their progression on Saturday only to concede an 88th-minute equaliser to Hungary in Marseille, with Birkir Saevarsson diverting Nemanja Nikolic's low cross into his own net.
They stand on two points and while a win against Austria will be enough, a draw may also see them through.
Hallgrimsson said: "We are lucky that we are in the last group so we can see if one point is enough or if we need to go for the win.
"We are in a good position as we will know the permutations before the game. We are fortunate in that respect. Even though we'll always go for the three points it is good to know if we need to take risks."
There would have been no need to consider a third-placed finish had Iceland held on for a little longer at a boisterous Stade Velodrome.
And although Hallgrimsson was disappointed with his side's use of the ball, he refused to criticise them and instead heaped praise on Hungary.
"The atmosphere was a bit down after the game as it would be for any team that concedes that late," he added.
"We were happy with a point against Portugal but we are really disappointed with a draw against Hungary.
"I’d like to give credit to the Hungarians and their coach, they are a really good team and those who underestimate them will suffer.
"They worked us around and we had to defend the whole game. We didn't use the ball as well as we should have but that was probably down to tiredness in the end.
"They outran us. [Hungary coach] Bernd Storck put two strikers on, and took one player from the defence. We should have punished them for doing that but sometimes when you take risks you succeed so all the credit goes to them."
Hallgrimsson accepted Iceland's penalty - converted by Gylfi Sigurdsson - was "a little soft" and deflected any blame away from the unfortunate Saevarsson for the own goal.
"I have seen a replay, I don't think he could have done much with that," he said. "There was a man behind him that would have scored so we can't blame him, the mistake was done before the cross."
Despite his obvious disappointment, Hallgrimsson still believes in Iceland's chances of advancing.
"We have to be upbeat," he said. "We are the only team never to have lost in the finals so let's hope that continues.
"It's good not to have lost. We are still in it, we have two points with a game to play. We were so close to securing it today and that’s what's so disappointing. Maybe tomorrow we will be happy with a point against Hungary."