Goal reported in August that Arsenal were in the market for Di Maria, and striker Karim Benzema, but they were met with resistance from the Spanish club.
Knowing that los Blancos had to sell to finance the £86 million purchase of Gareth Bale, however, the Gunners went back in for Mesut Ozil and tied up a deal on the final day of the transfer window, and Ancelotti has revealed why he was happy for the German to leave.
"He has less quality than Ozil but, for his character and the way he helps the team, I wanted him. With the arrival of Bale I thought it was more important to have Di Maria than Ozil.
"[Bale] wasn't cheap but that's the price of the market. It was the wish of the player that brought him here. Tottenham offered him more money."
Ancelotti also believes it is Cristiano Ronaldo's time to win the Ballon d'Or this year, ahead of Lionel Messi and Franck Ribery.
The Portuguese star has played second fiddle to Barcelona ace Messi since winning the prize while at Manchester United in 2008, with the Argentine claiming the last four titles in a row, but Ancelotti believes he deserves to win the latest crown for the all-round impact he has on the Spanish giants.
"It's Cristiano's moment to win it ahead of Messi and Ribery," he continued. "He has surprised me the most with his professionalism. He's very serious, he has amazing attention to detail. It's that which helps us the most - he doesn't just score."
The former Paris Saint-Germain and Chelsea boss also feels Bale has recovered from the injury problems that have hampered his integration at the Santiago Bernabeu, hinting that he could start the Clasico against Barcelona on Saturday.
"Since he's been here, he has not had a back problem," he continued. "The problem was his physical condition, as he hadn't trained. Now he's good, he's ready to play from the start. He could start against Barcelona.
"I asked him and he told me he prefers to play from the right. I think he likes playing from the right so he can shoot from his left foot."
Iker Casillas started the Champions League win over Valencia, but Ancelotti hinted that Diego Lopez will keep his place for Saturday's clash - though he insisted the club captain does not want to leave the club in January.
"It's a question for Iker, but I don't think he thinks like that," he said when asked if the Spain veteran would ask for a move.
"I have spoken with him to explain the situation. When he wants to talk to me, my door is always open. For a coach, to explain the situation is the most difficult.
"I already knew Diego Lopez. In 2006 I wanted to bring him to AC Milan. He started before the pre-season and was very strong. It wasn't an easy decision. Casillas gives me confidence and so I play him in the Champions League, these games are as important as La Liga.
"He is the captain, he has a lot of experience and he maintains the harmony in the team. Iker wants to stay at Madrid and this is good for us. But I've made my decision."
Finally, Ancelotti claims his side will face a tough challenge against a confident Barcelona side this weekend, adding that he will try to replicate last season's stunnig cup victory.
"Barca play with a lot of confidence because they've changed practically nothing," he added. "When Mourinho was here there were problems but they played fantastically there [at Camp Nou]. I will try to play like the semi-final of the Copa del Rey last year, the 3-1, and not change anything."