Despite losing 1-0 at Arsenal on Sunday, Norwich City's goalless draw at Chelsea later in the day left Pepe Mel's men three points clear of the relegation zone with a significantly better goal difference than Neil Adams' side and a game in hand.
Even if West Brom were to lose both of their remaining fixtures and Norwich beat Arsenal on Sunday, it is improbable that The Hawthorns outfit could be dragged into the bottom three.
And Morrison admits it is a considerable weight off the squad's shoulders.
"It was a huge relief over the weekend," he told the club's official website. "Obviously we know we’re not mathematically safe yet, we've still got jobs to do and we want to finish on a high.
"But that pressure is off us now, it’s been hanging over us for a few months. It's been difficult to play under.
"We've got two good games and we want to finish as high as we can."
West Brom travel to Sunderland in the Premier League on Wednesday knowing a point would see them mathematically safe.
