The Blues were poised to move four points clear at the top of the table on the back of centre-back Branislav Ivanovic's injury-time strike in the first half.
But Victor Anichebe is proving something of a super sub of late for Albion because just nine days after coming off the bench to equalise in a 1-1 draw with Liverpool, the Nigerian repeated the feat against Chelsea.
Mourinho feels Chelsea should have been out of sight before the Baggies mounted their fightback in the closing stages, with Anichebe netting his third goal of the season in the 87th minute.
"For 60 minutes there was only one team, and that team couldn't kill the game, especially in the first 15 minutes of the second half," said Mourinho.
"For (the next) 10 minutes the game was poor, and then for the last 20 minutes only one team and that team fought a lot to get the goal and the point, and in the end they deserve it.
"In the first half we had complete control without creating many chances - Petr (Cech) not making one save, their strikers with not one shot.
"In the second half they opened and gave us the space we didn't have in the first half, but we were not strong enough to kill the game.
"They had a reaction and we couldn't cope with the reaction. The team stayed back, we were too deep.
"I thought even if I sent on some attacking players it wouldn't help because we were under pressure. It was impossible for my defenders to get out of the first third of the pitch.
"They started putting long balls into the box, with some free kicks, corners and rebounds, and fighting for those, and they deserve."
Asked why his team sat too deep, Mourinho replied: "A little bit of a lack of personality.
"We must have the personality to get out, to not accept the pressure.
"The game could perfectly have ended 1-0, but we have to give some truth to their reaction."
Mourinho has been at pains to play down his team's title chances of late, despite their 1-0 win at championship rivals Manchester City and 3-0 thumping of Newcastle at the weekend.
Suggested this was a performance that underlined his 'little horses' claim, Mourinho added: "Yes. A ready team, a complete team kills this game. 2-0, goodbye, but we didn't."
Mourinho, meanwhile, refused to condemn the Albion supporters for their treatment of Ramires whose every touch of the ball was greeted with a chorus of boos.
Ramires was the player who contentiously earned Chelsea a penalty in the 2-2 draw at Stamford Bridge in October when Albion were seconds away from a shock victory.
At one point when he went down under a challenge from Thievy Bifouma which resulted in him requiring treatment it resulted in a chorus of 'Let him die!" and even louder jeers when he returned to the pitch.
"That's football. I don't think it's fair, but that's football," said Mourinho.
"Next season maybe they (the fans) forget and it doesn't happen the same.
"Everything the fans do, unless there is a lack of respect with race in this kind of situation, which for me was not the case, it was just booing. That's football."
For Albion head coach Pepe Mel, whose side are back out of the bottom three, he admitted this was his team's best performance from his five games in charge.
"I'm proud of my players," said Mel.
"In the first half we defended well, limited Chelsea's chances, and in the second we counter-attacked well and showed a good mentality.
"If we had scored earlier then we would have won the match, so for me this was our best performance against a good Chelsea team who are top."