Spurs came from behind to beat their local rivals 2-1 and Mourinho praised his side for coming out on top in a game of small margins against Mikel Arteta's Gunners.
The 57-year-old manager told Sky Sports: "I think the game was close.
"I think they hit the post, we had a fantastic shot from Ben [Davies] on the post, a couple of chances.
"I think the game was more tactical, I think Mikel found a way to find them to play and be stable and improve. They are improving.
"We felt we should adapt slightly to them and we did it very well."
Mourinho praised Spurs for shackling the threat of Arsenal full-backs Kieran Tierney and Hector Bellerin and pointed out that his team had 48 hours less to prepare for the fixture than their rivals.
He said: "How many times did Tierney or Bellerin reach the last third? I think we were very controlled today at that level.
"Even in the second half, when they had more of the ball and they were more in our half, we were quite comfortable in that situation.
"Great spirit, real heart, Arsenal had 48 hours more than us to rest, so it was hard."
Arteta claimed that his team had been in "total control" of the match and felt that defensive errors cost Arsenal victory.
The Spanish coach said: "The game was ours, we had total control again.
"The small details cost us, That's the biggest part we have to improve as a team."