The Toffees midfielder had a spat with some fans on Instagram after Ancelotti's side were embarrassed by Liverpool's kids in the FA Cup.
Speaking in his pre-match press-conference before Everton's home tie against Brighton on Saturday, the Everton manager said: "I spoke and the club spoke with him and it was a mistake - he shouldn't do a reaction like that.
"But after the game everyone is emotional and you can make a mistake like that."
Everton had just lost 1-0 to their arch rivals who fielded a weakened team at Anfield before Delph reacted.
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