The draw -- their 11th of the season -- extended their undefeated Premier League streak to 19 matches.
United last lost a league game in October when they were humbled 4-0 by Chelsea at Stamford Bridge, and Mourinho is enjoying his longest unbeaten run in the top flight since October 2005 when his own Chelsea side went 40 games without defeat.
But his side are still four points short of the fourth Champions League spot, having won only four and drawn eight of their last 12 league games at Old Trafford.
And the United coach was left lamenting his side's inability to kill off opponents.
"We have a lot of draws this season," Mourinho told BBC Sport. "Teams come here just to defend, goalkeepers come here to be man of the match.
We cannot score a goal even when we are one-on-one. We beat everyone on quality of play and direction of the game, possession, creation and ambition, but we drew too many matches.
United enjoyed 75 percent of the possession against Tony Pulis's disciplined Albion, but while they took 18 shots to the visitors' three, they failed to break down their opponents' back line.
Read the full article on eurosport.co.uk: Mourinho laments lack of killer instinct as United stumble