Stanley stay four points clear of the relegation zone after a 1-1 home draw with Mansfield.
Jake Speight put the Stags ahead in the 75th minute and they looked on course for a win until Kal Naismith converted a penalty deep into injury time.
"We have got to keep working hard as we are not mathematically safe yet," said Beattie, whose side were bottom of the table in October.
"We are all battling to keep this side in League Two and I am 100 per cent confident we will do it.
"The lads have been tremendous and they have a real never-say-die attitude. We have picked up a lot of points with late goals and it shows our character. They never know when they are beaten and they make me smile."