The Magpies bounced back from their 3-0 derby defeat to Sunderland to claim a point which took them six points clear of the Premier League drop zone.
And Perch is confident Newcastle will soon kill off any lingering fears of relegation if they repeat that performance in their final four games.
He said: "If we keep playing like that we will be fine. We have got a good enough team, we have got good enough players in the squad to make sure we don't go down.
"It is looking like it is going to be a low-points survival this year, but we still want to hit that 40-point mark to be sure.
"We just hope we keep playing well and picking up points away from home, and make sure our home form is a bit better."
Perch added: "If nothing else we had to show the fight and desire we were lacking against Sunderland.
"That is the bare minimum of any game - work-rate and desire to win the game.
"We lacked that against Sunderland and we knew we had to put it right."
Perch was involved in one curious incident in the final minute of the first half when he was penalised by referee Mike Jones for a foul on Billy Jones.
A free-kick was awarded on the right edge of the box but replays suggested the officials had blundered twice with the challenge inside the area but the ball being won cleanly.
Perch said: "It shouldn't have been given. I know it wasn't a foul but Mike said to me at the start of the second half that he called it right, it was a foul outside the box.
"The linesman didn't give it. It was the referee who was 20-25 yards away. I don't think it was his decision to make and I think he made the wrong one."