United were held at Old Trafford for the eighth time in 15 Premier League games this season as they failed to turn dominance of possession into clear-cut chances against a visiting side happy to sit back and defend the final third.
Mourinho's side managed 18 shots but only three on target as they found their attack blunted by West Brom's strong defending, and David de Gea almost spilled a Darren Fletcher effort into his own net in the closing minutes to compound United's disappointment.
But the former Chelsea boss, who was seen smiling with Pulis at the final whistle, took exception to the suggestion that United and West Brom cancelled each other out with their different approaches.
"What do you mean by that?" the manager replied when asked the question by BBC Sport.
After the question was rephrased, he responded: "You think so? Really? You think that's a question?
"I'm smiling because he [Pulis] is my friend. I was not speaking about the game. You think the game was like that? I can smile if I win, I can lose or draw. You think the game is like what I said?
"I'm sorry to say but it's a silly question. When the team crossed the midfield line once in 90 minutes and the other team is for 90 minutes with the ball, in the opponent's half, trying and trying and trying and trying, you are telling me that one team cancelled out the other one?
"We didn't have to defend. We had the ball all the time and David de Gea was sleeping, and because he was sleeping, he made that funny thing. I was laughing with that funny thing because it's the only way to react to that."
United will be six points off the top four if Manchester City defeat Arsenal on Sunday.