Wins for fellow strugglers Stoke and Portsmouth and a point for Blackburn did the Magpies no favours and they are now two points adrift of safety with eight games remaining.
However, Nolan is confident his team have what it takes to avoid the drop.
"There are no sirens going off here just yet," he told the club's official website.
"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.
"It's down to us now to start being ruthless - ruthless with each other and against teams.
"Even though we are in a sticky situation at the moment, I am 100 per cent positive we will still be in the Premier League come the end of the season."
The former Bolton captain, who returned from a three-game suspension on Saturday, admitted Newcastle were guilty of not taking their chances against the Gunners.
"Against Arsenal you have to take your chances and we had plenty in the first hour," he added.
"That's why they are a class side because if you don't punish them they will punish you.
"But if we can produce what we did in the first hour for 90 minutes then I'm sure we'll get out of it."