The Argentina international arrived at Old Trafford last week for a British record £59.7m fee after the arrivals of Toni Kroos and James Rodriguez saw him fall down the pecking order at the club.
But speaking on Sunday, Ancelotti, who praised the 'respectable' Xabi Alonso after he moved from the Bernabeu to Bayern Munich, launched an attack on Di Maria.
Although he did not name Di Maria, the Italian boss inferred that the 26-year-old was not prepared to stay and fight for a place in the side.
"Some players love to compete, others prefer to make more money," Ancelotti told Eurosport.
"If a player needs motivation to play at the best club in the world, I have no problem in letting him go."
Di Maria had a solid if unspectacular debut for United
Di Maria had a solid if unspectacular debut against Burnley, providing one brilliant pass for Robin van Persie before hobbling off in the 0-0 draw at Turf Moor.
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