The Blues, in much the same way as they ground out a point at Manchester United earlier in the campaign, were happy to leave Emirates Stadium with a share of the spoils in a 0-0 draw.
Both sides were unable to produce their free-flowing best, with greater emphasis placed on the need to avoid defeat rather than the desire to take maximum points.
Mourinho concedes that he set up his team to ensure that Chelsea did not leave empty-handed and believes they were comfortable throughout against a side that has topped the Premier League table for long periods this season.
He told Sky Sports: "Tactical match, a match that Arsenal wanted to win but didn't want to lose and Chelsea wanted to win but didn't want to lose.
"I think we could win because we had the biggest chance of the game, but we have goal-line technology and no-one complained. I think they had one chance in the second half, the goalkeeper is not in the game.
"The game, I thought, was completely controlled by us. We gave them the ball, we let (Mikel) Arteta play free and pass the ball from side-to-side.
"It was important for us this match not to lose because it is one thing to be two points behind the leader and another to be five points behind the leader. It was very important for us. Both teams were worried about losing."
The Portuguese tactician added: "Football is not about set-up, it is about what happens in the game. The biggest chance was our chance and the chances we couldn't make into big chances.
"Our half-chances, we had lots of space to counter-attack and because of a bad choice we were not aggressive enough to attack the defenders and go for the goal. They had one chance in the last part of the game. We had it completely under control."
Mourinho insists he will not be favouring a defensive style in his second spell at Stamford Bridge, but appreciates that certain fixtures require a different approach.
He said: "I want Chelsea to go in another direction, that was our plan and what we want for Chelsea's future. I am not building a team for one season, I am building it for a long period.
"There will be some matches where I have to take one step back because of the opponents and play sometimes for a result. Today was the kind of game where it was important for us not to lose."