Newcastle's 3-1 home defeat by Arsenal on Saturday saw the Magpies drop into the relegation zone as fellow strugglers Stoke City and Portsmouth both won and Blackburn Rovers drew.
Only North-east neighbours Middlesbrough and seemingly doomed West Bromwich Albion are below them and with only eight matches to play and a difficult run-in to come, Newcastle are two points from safety.
However Nolan, signed from Bolton Wanderers in the winter transfer window, told the Newcastle's website that "there aren't any sirens going off yet.
"I'd far rather be in the bottom three now than at the end of the season. I think we've got enough in the locker and enough in the changing room to get us out of this in the next eight games," he said of a talented squad.
"It's down to us now to start being ruthless - ruthless with each other and against teams.
"I am 100 percent positive we will still be in the Premier League come the end of the season."
Newcastle's plight is not helped by manager Joe Kinnear being sidelined after heart by-pass surgery and doubts over his long-term involvement with the club because of his health.
Newcastle, one of the best-supported sides in England, have not won in their last five matches under caretaker Chris Hughton, but he is keeping as optimistic as he can.
"The moment the players see worry in me will not be a good reflection on what I am trying to do," he said after Saturday's defeat.
Newcastle were promoted to the Premier League in 1993, the second year of its existence, and finished runners-up in 1996 and 1997.
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