After scoring 19 times in their four previous matches, Mourinho's side were cautious against the Clarets, with the manager preferring Lucas Moura, Moussa Sissoko, Matt Doherty and Ben Davies over the likes of Gareth Bale, Giovani Lo Celso, Serge Aurier and Sergio Reguilon.
"This is the kind of match with ingredients to lose points," Mourinho said afterwards. "Monday night, empty stadium, cold rainy night, an opponent that defends very, very well and copes well with the attacking power of an opponent like us.
"Ingredients to lose points unless you want very, very much to win matches, which is when you can do something special. Europa League, Premier League, doesn't matter what – I want the team to go to every match to win.
"Then you lose, draw but you go to win it. This is something special I believe, because it's a change in mentality, a change of philosophy.
"But tonight was the kind of match I knew from the beginning, I've come here since 2013, I know Sean [Dyche], I know Burnley and I know how it is to play against them and I knew we couldn't play the way we like to play.
"But we cope well with difficulties Burnley gave us on the pitch and three important points for us."
As Spurs searched for a goal in the second half, Mourinho left summer signings Bale, Reguilon and Carlos Vinicius on the bench and did not call for Lo Celso until the 80th minute.
His first change on the hour, Erik Lamela, did make an impact, however, with the Argentine's corner flicked on by Kane for Son to head home at the back post.
"I was speaking to [assistants] Joao [Sacramento] and Ledley [King] about changes during the match but in the end we need to keep the balance," Mourinho said. "This is the kind of match where if you risk too much you have the risk of losing it.
"And with the level of the attacking players we have, even not playing well and creating lots of chances, there is always the chance to score a goal, which we did. And the last 15 minutes we managed the game very well."
Kane has now assisted all but one of Son's eight League goals this season and Mourinho said their connection was based on a long-term understanding and selflessness.
"They played together for a long time and that immediately gives a good understanding between the players," he said. "The way we're trying to play I believe goes in the direction of their qualities. They're enjoying.
"They're very good friends which I think is very important. When you have top players in the team, it's important that their personal relations is also very good.
"Because in the end there is no egos, I score you score, doesn't matter who. What matters is the team, the club."
Dele Alli was among nine senior players not included in Mourinho's 18-man squad, also including Harry Winks and Davinson Sanchez.
"I feel sad every time I have to write a list of players selected for a game," the Portuguese said. "It's not just about Dele. But if the players understand Thursday we have another match and that some people who didn't play are going to play Thursday.
"And vice versa. This is the life of a big club, the life I know from my times in Real Madrid, Inter [Milan], Chelsea. I know that."