Juan Mata put United ahead at Old Trafford on Saturday in the 68th minute, but Olivier Giroud headed home with one minute of normal time left to ensure the spoils were shared.
It is a third successive league draw at home for Mourinho’s side, with the Premier League title challengers now languishing in sixth.
And the Portuguese manager is growing frustrated by United’s recent misfortunes, telling Sky Sports: “We are the unluckiest team in the Premier League.
“In the last three matches at home, against Stoke we have to win 5 or 6-0 and we draw, against Burnley we have to win 5 or 6-0 and we draw and today we have to win 2 or 3-0 and we draw too, so I think we are the unluckiest team.
“But the team is playing well, the team is working really well.”
Mourinho felt his team were worthy of all three points at Old Trafford, hailing the way they stifled Arsenal with a strong showing in defence.
“We were the best team by far. I don’t want to say they didn’t want to win, but they had no chances to win,” he continued.
“They couldn’t be Arsenal the way they normally play football. We were phenomenal defensively – the way we pressed, we were very strong without the ball, controlled their counter-attacks, their best players.
“When we had the ball we were very comfortable. We played quality football, we scored a fantastic goal. We had chances to kill the game. The Marcos Rojo and [Paul] Pogba situations for the 2-0 were open goals and then the only time we had a situation that we couldn’t resolve they scored the goal.
“So they were the lucky ones and we were unlucky, but that’s football.”
United had appeals for a penalty turned down after Antonio Valencia went to ground under a challenge from Nacho Monreal, but Mourinho would not lay the blame for the result with referee Andre Marriner.
“I don’t want to speak about it. I have a very good feeling with Andre Marriner, he is the kind of referee that if he makes mistakes against my team I know that there is no intention,” he concluded.
“I remember the words he told us before the game in his dressing room: ‘I don’t want to be seen, I want to do my work and you to help me do it the best I can.’
“He doesn’t want to be the star of the game, he’s an honest man and a good referee. If it was a mistake, I don’t want to say yes or no – I know because I’ve watched it on video a few times – but I don’t want to say because he’s a referee and he’s trying to do his best.”