United knew avoiding defeat against the league's bottom side would have delayed its city rival's coronation again, having battled from two goals down to win at the Etihad last weekend, but they turned in an insipid performance which was duly punished by Jay Rodriguez's 73rd-minute header.
Mourinho's side twice came close through Romelu Lukaku but they scarcely threatened the Baggies over the course of a turgid 90 minutes.
The Portuguese was unimpressed with his players' efforts and attacked their lack of fluidity and desire to take too much touches.
"I think we were deservedly punished," he said.
"We were masters in complication, everything was complicated.
"We didn't want [to play] or couldn't play simple, everything was slow, one more flick, trick, turn.
"There was no fluidity. We did not deserve to lose, but we gave them opportunity to win the match."
A stirring comeback against Pep Guardiola's men last weekend prevented United's neighbours from winning the title and Mourinho suggested that dramatic result created complacency in his side.
"I won eight titles and I am not [over] the moon because I won against Manchester City," he added.
"I saw lots of people [over] the moon because we won against City. You could see the difference in the attitude to players compared to last week.
"We deserve to be punished, but the defeat was too heavy."
Juan Mata echoed comments from Mourinho, accepting United were far below the required standard in defeat to West Brom.
"It's a big disappointment. A bad day and a bad result," Mata said. "Everyone is disappointed. We didn't play well at all and it's a bad afternoon for us.
"After beating Manchester City we wanted a winning spirit until the end of the season but today was one of those days. We didn't create enough chances to score and West Brom were fighting for survival.
"It hurts [for Manchester City to win the title]. Our aim is to keep this second position. It is not ours yet and we need to be very clear about that. Today was a very bad day and we need to move on."
"Football is an unpredictable game. Sometimes, these things happen."