Juric takes charge with Saints sitting bottom of the Premier League table at Christmas. Only four teams have beaten the drop from the same position, though all had ten or more points more than Saints at the same stage.
"It will be a very tough job and I know that in the history nobody stayed in the Premiership with this situation, but I think there are a lot of good players, and we have to be much better in some moments of the game," said Juric.
"I am optimistic. I'm really optimistic. Even the other day, I saw their mentality and it's the first step to doing better. I think we can do something exceptional. The guys have to be very motivated to do something that never, nobody did."
Juric also said: "It was a little bit of a dream, the Southampton opportunity.
"I was thinking that life is short, I want to try new things and I want to travel to the other way of working, put myself in a difficult situation, and that's it.
"They don't know me but I know them. I said that I believe in them, they have quality, they can do it. Be positive, work hard, and everything is possible."