The result left United in fifth on 53 points from 28 games, four behind fourth-placed Manchester City who visit Arsenal on Sunday. West Brom stayed eighth on 44 points from 30 matches.
"We have a lot of draws this season," Mourinho told the BBC after his side produced a toothless performance despite enjoying the lion's share of the possession.
"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," he added.
"We beat everyone on quality of play and direction of the game, possession, creation and ambition but we drew too many matches."
United, who were missing six regular starters through injury or suspension, stretched their unbeaten league run to 19 games but it will be scant consolation after they failed to carve out any clear-cut chances.
The home side, whose final pass kept going astray, had to wait until the 67th minute for their first shot on target when keeper Ben Foster denied Henrik Mkhitaryan.
Foster kept out two long-range Marcus Rashford strikes in the closing stages either side of West Brom's best chance, when former United midfielder Darren Fletcher almost stunned United keeper David De Gea who had a very quiet afternoon.
Fletcher hit a looping shot from distance which De Gea fumbled and was relieved to see the ball bounce off the woodwork and back into his arms.
While he tried to make light of De Gea's error, a frustrated Mourinho also bemoaned West Brom's tactics based on a stonewall and well-organised defence.
"David de Gea was sleeping and he did the funny thing at the end, I was laughing with that," he said.
"One team had the ball, one team didn't. One team tried to win, the other tried to draw. One keeper did a funny thing, the other made three great saves."
He also hit out at the media after being asked if he thought the game was balanced.
"You think the game was equal? I can smile win, lose or draw. I am sorry to say, it is a silly question."
(Writing by Zoran Milosavljevic; Editing by Ed Osmond)
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