Olivier Giroud's late header was enough to snatch Arsenal an undeserved point at Old Trafford, after Juan Mata had given Manchester United a second-half lead.
The draw left Mourinho bemoaning his side as "the unluckiest team in the Premier League," a result that sees United languishing in sixth place, eight points behind leader Liverpool.
"Of course it is two points dropped. We were the best team by far," the 53-year-old told Sky Sports. "They had no chances to win. They could not be Arsenal the way they normally play football.
"We were phenomenal defensively. We scored a fantastic goal, we had chances to win the game and then the only time they go there, and the only time we had a situation we could not resolve, they scored.
"They are the lucky ones and we are the unlucky ones. The team played very well. This team at the moment is the unluckiest team in the Premier League. That is the reality. The team is playing well.
"I am happy with the work and the guys and I am super happy with the fans. They are amazing. They know to be fair and applaud a team that has dropped two points."
United went ahead midway through the second half after Paul Pogba's pass found Ander Herrera on the byline. The Spaniard cut the ball back into the path of his onrushing compatriot, and Mata coolly placed his shot into the far corner.
With the home side in control for prolonged periods, the win looked secure as the clock slowly ticked towards 90 minutes.
Marcus Rashford was the hero in this fixture last season, terrorizing the Arsenal defense to score twice in a 3-2 win.
However, the baby-faced striker was arguably at fault for Arsenal's equalizer, allowing England teammate Alex Oxlade-Chamberlain to easily breeze past him and stand up a cross for Giroud to head home.
Incredibly, the Frenchman, who has had to settle for a place on the bench behind Alexis Sanchez this season, has hit the target with his last nine shots in the league -- scoring eight.
Understandably, despite the draw meaning Arsenal missed the chance to close the gap at the top of the table, Wenger was happier with the result than his Portuguse counterpart.
"The result in the end is positive for us because we were 1-0 down with two minutes to go," the Frenchman told Sky Sports.
"Our passing was not quick enough, our penetration was not there and in the end we looked like we had good possession of the ball but not many chances. The players who came on made a massive difference today.
"When you are 1-0 down and come back to 1-1 of course you have to feel happy. We lacked a bit of sharpness today, what is it down to I don't know, but at least we came back."
Arsenal's last Premier League win at Old Trafford came a decade ago and, when asked, Wenger admitted his players may well suffer a mental block when playing there.
"It's funny you tell me that because I wondered during the game about that. And honestly, you never know.
"In the second half in the first 20 minutes we suffered. We came out of the dressing room in the second half, I think we suffered for 20 minutes and they deserved to be in front.
"Last year we would have lost maybe this game and today we didn't lose it. So we have improved on that front. We have shown steel. We want style and steel, and we had more steel than style today."
Yaya Toure inspired Manchester City to a hard-fought win against Crystal Palace on his first start for the club since March.
The Ivorian's agent, Dimitri Seluk, has been involved in a very public dispute with manager Pep Guardiola since the start of the season.
Guardiola took offense to several of Seluk's comments and vowed to leave Toure out of the squad until one of the two apologized.
Toure obliged at the start of November, saying sorry for "misunderstandings"
and today -- two weeks later -- was included in the starting XI for the first time in nine months.
The 33-year-old gave City the lead five minutes before half-time, exchanging an rapid one-two with Nolito, before unleashing a ferocious shot into the top corner.
Connor Wickham got the home side level just after the hour mark, but shoddy defending allowed Kevin De Bruyne's corner to roll into the six-yard box for Toure to tap home the winner.
"To be honest, I just want to help the team and make the team succeed," Toure told the City website. "I'm really happy for the three points and for the lads because today, we've fought here."
Toure's teammates applauded him as he entered the changing room, which, he says, meant a lot.
"They have always been brilliant with me, always supportive. I'm very delighted for the team and the three points were deserved."
Guardiola echoed the sentiment of his players, calling Toure "a part of history" at the club.
"Of course his performance was great for the two goals, but not just for that -- nobody has doubts about his quality. In the last month and half, his training and physical condition is perfect, he's like a young guy again.
"I'm so happy for him and his family. Yaya is a part of history of this club. He is so, so important, he is a player with a huge personality and the people and teammates appreciate him a lot.
"He's now a real part of the team. He can help us achieve our target."
The win sees City go level on points with league leader Liverpool, after Jurgen Klopp's side struggled to a goalless draw away at Southampton.
Meanwhile, reigning champion Leicester City continued its poor start to the season with a 2-1 defeat away to Watford. The defeat leaves Claudio Ranieri's side precariously perched just two points above the relegation zone.
Tottenham has the chance to close the gap on Arsenal in fourth when it faces West Ham in Saturday's late kick off, while Chelsea will return to the top of the league with victory against Middlesbrough Sunday.