West Brom are currently languishing at the bottom of the Premier League table, having won six of their 25 games so far this season.
Tony Mowbray's side have not won a league game on their travels since September, but Morrison says they will have to start recording some victories away from the Hawthorns in order to beat the drop.
"We may need six more wins to stay up so we'll need to win one or two away from our place. But it's possible looking at our remaining fixtures," the 22-year-old said.
Working"It's not nice being where we are and we don't want to be in the Championship next season. The Premier League is the best league in the world and we're all working hard to try to stay in it."
The Scotland midfielder recognises that they will have to erase the lapses in concentration that have marred recent games if they are to achieve his aim.
"But we need to stop conceding goals just before half-time in games. It happened again last weekend against Newcastle," he added.
"We've done it in our last four away games and last two home matches in the league.
"It's making life difficult for us and we need to try and put that right over the next 13 games. Bad mistakes cost us again against Newcastle."
InjuryMorrison is struggling with hamstring and groin problems at the moment but is hoping the club's short training camp in Spain can aid his recovery
"I've just been working in the gym because I can't train on the indoor surface which the rest of the players have been using because of the bad weather.
"We'll be working hard over in Spain and hopefully, we'll come back fresh-minded, have fresh legs, and be raring to go."