The manager told BBC Radio Solent: "I think the overall team performance was amazing today. To beat a team such as Everton, a team that is playing so well, you have to have an amazing overall performance, and that is what we had here today.
"I'm pleased in the way that we played today and how we performed against a team that has won seven out of eight and is trying to break into the top four and break into the Champions League.
"We played very well against them and the overall team performance was very good so I am very pleased with that."
Southampton travel to Swansea City next Saturday.