Carlo Ancelotti hailed the 1-0 victory over Southampton as a "really important" win as Everton closed the gap on the top four.
The Blues won at Goodison in the league for the first time since December thanks to Richarlison's ninth minute goal.
Everton dominated most of the first-half but could not add to their lead which gave Southampton renewed hope in the second-half.
The Blues were indebted to Jordan Pickford's save in the final minute to deny Jannick Vestergaard to keep their lead intact.
"It was a really important win," Ancelotti said. "The expectation was that we would win and we did it, with a good performance.
"And with a strong team work from all of the players, and I am really pleased for this.
"Calvert-Lewin didn't score but he did a fantastic game. We worked hard, we were really strong defensively and, at the end, we deserved the win."
On Richarlison, who was told by Ancelotti last month that he needed to work harder, the manager said: "He's answering [the challenge] this is true but Richarlison is this.
"He is not doing something extraordinary now. In my opinion he is doing his job.
"He is a player with this quality and so I hope, and I am sure, he is going to continue."
