Chelsea, who had won nine of their last 11 games in all competitions, were expected to make light work of a West Brom side languishing in the bottom three.
The league leaders looked in control until the closing moments but it was their inability to handle the late pressure which frustrated Mourinho.
"In the last 20 minutes they put us under pressure and they scored a goal as a consequence. Maybe they deserved that point. A point is a point and at the end of the season we will see," he told the BBC after his side moved on to 57 points.
"I think the game for 60 minutes was completely in our hands, West Brom didn't put one foot in our box. We couldn't kill the game."
The 51-year-old Portuguese has consistently played down Chelsea's title credentials, labelling them a 'little horse' in the race with second-placed Arsenal, who are two points behind, and Manchester city, who are a further point back in third.
"I was feeling that the only thing we could do is defend well. We were not strong enough to get out in the last 10 minutes. The game doesn't end until the last whistle and the defensive mistake led to the goal," he added.
Mourinho was at least able to welcome back striker Fernando Torres, who was a 69th minute substitute for Samuel Eto'o, after he was sidelined since suffering a knee injury on Jan. 19.
"He's one more option, for the last month we've had only Eto'o and Demba (Ba)," he told Sky Sports. "If we have all of them available then I think it's going to be more than enough."
West Brom coach Pepe Mel said his side could have taken all three points but needed to get back on level terms earlier.
"I am very pleased. The players worked hard and were strong. If we scored the goal earlier, we would win the game," he said.
"Chelsea were in front, for me today is a good day. The players performed very well and, for sure, if we scored a goal before them, we would win the game."
Since Mel took over from Steve Clarke in January, West Brom have taken points from Everton, Liverpool and now Chelsea despite trailing and he was confident they would stay up.
"One-one against Everton, Liverpool and Chelsea. Now we need to win our next game. West Brom next season will be in the Premier League," he said.