Last week's humiliating derby defeat by Sunderland, coming soon after the disappointment of Europa League exit, raised concerns about morale among Alan Pardew's men for the run-in.
Newcastle had travelled to West Brom for their latest game just five points above the Barclays Premier League relegation zone.
But even though they surrendered an early advantage to draw 1-1 at The Hawthorns, Perch feels the performance was good enough to suggest problems will be solved.
Perch 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."
Newcastle showed an early determination to make amends for the Sunderland debacle and grabbed an eighth-minute lead with a glancing header from Yoan Gouffran.
The visitors then squandered a number of chances to increase their advantage before the break, most notably when Papiss Cisse seized on a poor Jonas Olsson pass only to clip over.
Newcastle were made to pay for their profligacy as West Brom fought back in the second half, hitting the bar through Romelu Lukaku before Billy Jones levelled just after the hour.