Oliver also sent off Spurs midfielder Erik Lamela in the second half for two yellow cards.
After the game, Mourinho criticised the decision to award a penalty and suggested Oliver could have been fatigued after refereeing Dynamo Kiev versus Villarreal in Ukraine on Thursday.
Mourinho said: “If somebody has a different opinion [on the penalty], it has to be an Arsenal season-ticket holder. He is the only one I would accept a different view because that is the passion speaking, apart from that I would not accept that anyone has a different view. Because it is too obvious.
“It was a mistake by Michael Oliver. Players get tired of so many matches, coaches get tired, referees maybe get tired. He had a game midweek in the Europa League, maybe [he is] tired.
“Normally I am very unlucky with him because my record with him on penalties is astonishing. Chelsea, Manchester United, Tottenham, it does not matter the club I am very unlucky with such a good referee.”