Ancelotti saw his men fall behind at St Mary’s with 27 minutes on the clock in the Premier League encounter when a fierce James Ward-Prowse effort beat Jordan Pickford in the Toffees goal.
Gylfi Sigurdsson had hit the bar when it was 0-0, but Southampton were rarely troubled by the visitors and Saints made it 2-0 in the 35th minute through Che Adams.
The afternoon got worse for Everton in the 72nd minute when Lucas Digne was shown a straight red card after a challenge on Kyle Walker-Peters.
Ancelotti was unhappy with Digne being sent off and insists that Everton will lodge an appeal against the decision.
The Toffees boss also issued a warning to his players on a tough winter programme which is now looming and the importance of bouncing back.
“The red card was a joke, it was not intentional, for sure it was not violent”, Ancelotti said post match on Sky Sports.
“Maybe it was a yellow. Maybe all this talk all week against Pickford, against Richarlison, affected the decision and if so it’s not right, it’s not fair.
“We will appeal, for sure.
“I told the players winter is coming and we will have to react”, the Everton boss added.
Everton are next in action away at Steve Bruce’s Newcastle United, while their last game before November’s international break arrives is a home meeting with Manchester United.