Sunday's match was a sweet moment for Mourinho who claimed his biggest win since replacing Mauricio Pochettino in November, although he had raged before halftime, believing City's Sterling should have been shown a red card for a foul on Alli.
"It was a red card to Sterling," he said, adding he could understand given the pace of the game why on-pitch referee Mike Dean might give a yellow card.
"For me, Mike Dean [gave a] good performance. The problem is the VAR ... I thought I was going to love VAR the same way I love goal-line technology," Mourinho said.
Manchester City manager Pep Guardiola, whose clashes with Mourinho have been well documented, didn't directly respond on what he thought of his counterpart's claims.
"I don't comment on other manager's opinions. I don't want to comment on that [the Sterling incident]," the Spaniard said.
On beating old adversary Guardiola for only the sixth time in 23 clashes, Mourinho told the BBC: "It's a pleasure to get three points in a match where we knew it would be very difficult. I have better feelings for Pep than you can imagine. We worked together for three years [as assistants at Barcelona]."
Steven Bergwijn made an instant impact in his Spurs debut with a stunning opener in the win. The Dutch midfielder, signed this week from PSV Eindhoven, produced a masterful piece of skill to chest down and sweep home a volley three minutes after City's Oleksandr Zinchenko was shown a second yellow card on the hour.
With 10-man City stretched Son Heung-min added a second in the 71st minute with a deflected effort.
"[Bergwijn's] goal was a great goal and so important for us," Mourinho told reporters. "[It was] the icing on the cake of a very good performance. Independent of the goal his performance was very good, very solid, very mature."
City remain 22 points behind runaway leaders Liverpool and only had themselves to blame for a sixth defeat of the season as they wasted several gilt-edged chances and missed yet another penalty when Hugo Lloris saved Ilkay Gundogan's spot kick.
"[Liverpool] are unstoppable with a lot of points...now is the target for the [other] competitions and quality for the Champions League next season," Guardiola said. "The distance is so big and next season we have to do better."
Sergio Aguero was unusually profligate on Sunday, striking the post in the first half and missing two other chances as City failed to score in consecutive games for the first time under Guardiola.
"Always a belief you are close to winning the games when you create the chances," Guardiola said. "It's happened sometimes this season and we have to accept it. We lost the game and that is really all I can say."
Information from Reuters was used in this report.