Al Thani launched a furious online outburst on Tuesday night immediately following Malaga's 3-2 aggregate quarter-final defeat at the Westfalenstadion, which saw Dortmund score twice in stoppage time to claim a remarkable win.
Malaga, playing in the competition for the first time, were fuming with some of the decisions made by Scottish referee Craig Thomson and his team of officials, including Felipe Santana's 93rd-minute winner which he appeared to score from an offside position.
Al Thani on Tuesday night claimed on Twitter his side had been the victims of "racism", although it was not immediately clear at whom the accusation was directed, and urged UEFA to open an investigation.
And the Qatari owner returned to Twitter on Wednesday morning to continue to show his outrage.
"Yes, we were targeted from the beginning of the season by corrupt UEFA and based on racism," he wrote on his personal account, @ANAALThani.
In December, Malaga accused UEFA of unfair and unjust treatment after they were handed a one-season ban from European competition - to be imposed if the club qualify for the Champions League or Europa League during any of the next four seasons - due to outstanding debts.
Al Thani, who also posted pictures on Twitter of the offside decisions that had gone against his side as Dortmund scored their match-winning goal, was not the only person bitterly upset by Malaga's defeat.
Veteran winger Joaquin Sanchez, whose 25th-minute strike from the edge of the area had put Malaga ahead on Tuesday night, also hit out at UEFA and their president Michel Platini, telling Spanish radio station Cadena SER: "We suspect Platini and all of them there. Because we are Malaga and not Real Madrid, it's easier to do this with us.
"We're very hurt because we didn't deserve to go out in this way.
"We saw the footage of the goals after the game. Something like this shouldn't happen at this stage of the game, but of course, we are Malaga..."
Coach Manuel Pellegrini said after seeing his team's fairytale Champions League debut campaign end in disappointment and controversy: "Firstly, after we went 2-1 ahead, there appeared to be no refereeing.
"Our players were being elbowed and pushed all over the place. Two of their players should have been given a red card, and there was a double offside for their third goal.
"It was extremely difficult to regain possession under these conditions. We're all extremely bitter at the outcome."
He added: "There was no refereeing in the last seven minutes. The players were allowed to do whatever they wanted, which made it impossible for us to maintain our lead.
Defender Martin Demichelis said: "We're frustrated. There are ways of losing in this sport but when something happens like that it hurts much more. I'm convinced there there were two offsides."
Julio Baptista told his club's website: "We're going out with our heads held high. We've been superior to Dortmund in this game and we managed to play at a very high level and the truth is we have a bitter taste in the mouth due to the last goal of Borussia."