The visitors had struggled to get going as Saints were clinical, ending the Toffees’ unbeaten run, and they finished with 10 men following Lucas Digne’s red card 18 minutes from time.
Goals from James Ward-Prowse and Che Adams had given the home side a two-goal lead in the first half at St Mary’s.
Richarlison was sent off during the Merseyside derby last week, but when asked whether the Everton players were overstepping the mark following Digne’s dismissal, Ancelotti said: “No I don’t think so.
“No from the fact that from this red card we have to lose maybe Digne for three games, it’s too much. Of course we are worried, we are worried for this reason.
“We didn’t complain about Richarlison and he is out for three games, but here I think we have to agree that it was not the right decision.”
Everton playmaker James Rodriguez appeared to be holding his leg in the final stages, with Ancelotti having used up all of his substitutions.
But the Italian does not expect it to be a big issue, saying: “I think we have to check in the next few days, but he was tired at the end.
“He felt his muscle a little bit tired and a little bit tough but I don’t think it’s a big problem. It’s true that the game was difficult for everyone.”
Southampton goalscorer Adams hailed his side’s resilience during the win.
“It was a lot of hard work that we put in, and I think we deserved it in the end,” he told the club’s official website.
“I think we defended very well from the first minute. The first 20 minutes were very hard but we dug in and managed to get the win.
“We were very compact and hard to break down, and I think that’s what won it in the end. We kept possession very well at the end and dug in deep for the three points.”
Adams also stressed the importance of his and Danny Ings’ relationship, after the Saints’ top goalscorer turned provider on Sunday, recording two assists in a match for the first time in the Premier League.
When asked about the partnership, Adams said: “I think it just comes from playing games, getting to know each other and knowing each other’s runs, so I think it’s definitely important for the two of us.”
