Juan Mata was dismissed after just 26 minutes at The Hawthorns before Solomon Rondon struck to seal all three points for Tony Pulis’ side.
The result came as a setback in Man United’s ambitions to qualify for the Champions League next term but Carrick insisted his side can still finish fourth.
“It’s not out of sight,” Carrick said.
“We just need to get back to winning ways. It’s easy to say. We have big cup games coming up and we need to be ready to them.”
United are now sixth in the table, two points behind West Ham United and three points behind fourth-placed Manchester City.
There had been renewed optimism at United following a good run of victories but the loss against West Brom brought everyone associated with the club right back down to earth. United’s awful form away from home this term seems to have been their undoing.