Mourinho: United lost ambition in second-half slump
First-half goals from Romelu Lukaku and Jesse Lingard put second-placed United on track for their sixth win in seven Premier League matches.
But United eased off after the interval, with substitute Gareth Barry scrambling in West Brom's first goal under Alan Pardew to set up a nervy finale in Sunday's match.
Mourinho insisted his side still did enough to win the game while acknowledging West Brom battled back well in the second half.
"I think [United had] less ambition, the intensity in the first half maybe we didn't have in the second half," Mourinho told Sky Sports.
"Probably we lost a bit of ambition. But they are really powerful in the air - they have giants and aggressive people in the air.
"But after their goal we controlled the game again. We brought the ball into the opposition half and they didn't have much more after that.
"I think we deserved the win. We were the best team. I knew and the players knew that West Brom are very dangerous on set-pieces.
"[Former West Brom head coach] Tony [Pulis] is an expert on that - very strong and physical on set-pieces and we knew that it could be a problem.
17 December, 2016: West Brom 0 #MUFC 2
17 December, 2017: West Brom 1 #MUFC 2 pic.twitter.com/n1Cd7A1EB9
— Manchester United (@ManUtd) December 17, 2017
"We controlled the game for a long, long time, then Alan reacts with a few changes to try to give the team more width and quality with a second striker in the middle.
"We had a few chances to kill the game but I knew they would react. So when they scored it's normal, but we deserved the victory overall."
65' - Meanwhile, the Reds are forced into a change after @Anto_V25 picks up an injury. On comes Marcos Rojo for his 100th #MUFC appearance! #WBAMUN pic.twitter.com/kH1ii0Gs51
— Manchester United (@ManUtd) December 17, 2017
United were dealt a blow when captain Antonio Valencia limped off, with Mourinho blaming fatigue for the full-back needing to be replaced.
"That's football in England, especially in December," Mourinho added. "Players are not machines and sometimes it happens.
"He knew he was not going to play the next game [Wednesday's EFL Cup quarter-final at Bristol City] and he was asked for a last effort before the break but he couldn't resist.
"We have other players, [Daley] Blind and [Matteo] Darmian were not on the bench, and we have other people to cope with the difficulty."