Everton coach Carlo Ancelotti criticised referee Kevin Friend's "joke" decision to send off Lucas Digne as the Premier League leaders' unbeaten start to the season ended in a 2-0 defeat against Southampton.
Everton had gone eight games without defeat in all competitions this term, but they paid the price for a lethargic display at St Mary's.
Ancelotti's side fell behind to James Ward-Prowse's first-half goal and Che Adams doubled the lead before the interval.
Left-back Digne was sent off for a dangerous challenge on Kyle Walker-Peters in the second half despite his claims he tripped when he stood on the Southampton defender's heel.
"The red card was a joke, it was not intentional, for sure it was not violent. Maybe it was a yellow," Ancelotti said.
"It's not right, it's not fair. We will appeal, for sure."
Without the suspended Richarlison and injured Seamus Coleman after last weekend's stormy Merseyside derby draw with Liverpool, Everton lacked the drive and quality that had been the hallmark of their strong start to the campaign.
They remain above the champions and their local rivals on goal difference but Ancelotti admitted: "We didn't play well, Southampton were better than us and they deserved to win. I told the players winter is coming and we will have to react."
Southampton have only lost twice in 13 league matches and climbed within three points of first place.