A stunning strike from Son Heung-Min and a thunderous effort from Harry Kane clinched the points for a Spurs team who were reasonably comfortable throughout the match.
However, Mourinho had words of encouragement after the game for Arteta, who is now under big pressure after a bad run of results.
“I want to give a good word, congratulations to Mikel,” Mourinho told reporters.
“Because he gave us a very difficult game. Tactically they are very good.
“They are very well organised. They were trying to find the triangles on the side. They gave us problems.”