Digne made heavy contact into the back of Kyle Walker-Peters' ankle with 18 minutes to go in the 2-0 loss, resulting in a straight red card, a decision the France international protested.
Ancelotti felt Digne should have been shown a yellow at most for an unintentional challenge and queried whether negative publicity after the Liverpool game had proven to be a factor.
Everton came in for criticism following the derby after goalkeeper Jordan Pickford's challenge caused a serious injury to Virgil van Dijk, while striker Richarlison saw red for a foul on Thiago Alcantara.
"The red card was a joke," Ancelotti said about the Digne incident to Sky Sports. "It was not intentional, for sure it was not violent conduct.
"Maybe it could be a yellow. Maybe all the rumours all this week against Pickford and against Richarlison affected the decision and if it's like this it's not right - it's not fair. We will appeal, for sure."
The red card ended Everton's hopes of a comeback, but defeat was already looking likely after goals from James Ward-Prowse and Che Adams in the first half, both of which were set up by Danny Ings.
"I told the players winter is coming and we will have to react," the Italian added. "We tried to get back into the game, we had some good control after half-time.
"But we didn't play well, Southampton played better than us and they deserved to win. Sometimes you are not at your best.
"It was not a good performance. It came after a really good run for us - now we have to look forward with the same spirit and belief. It happens."
Everton's first chance to bounce back will come when they play away to Newcastle United next week.