Cape Town - David Moyes felt Manuel Lanzini's saved penalty was the turning point at Goodison Park on Wednesday as Everton claimed a 4-0 win over West Ham United.
Wayne Rooney had opened the scoring on 18 minutes with a rebounded header after Joe Hart had saved his spot-kick.
Rooney then added a second on 28 minutes before an improved second half from the Hammers that saw substitute Diafra Sakho win a penalty - that was saved by Jordan Pickford.
Rooney soon completed his hat-trick, on 66 minutes, with a first-time drive from inside his own half, following a poor Hart clearance before a 78th minute fourth goal from Ashley Williams.
"We were much better in the second half and I don’t think we deserved the scoreline in the end," speaking after the game, Moyes told the club's official website.
"Ultimately, we missed a penalty kick when it was 2-0 and I thought we were the team on top in the second-half."
He added: "I thought we played well in the second half and things didn’t quite go for us. Jordan Pickford saved a penalty; Joe Hart saved Wayne’s penalty but the rebound came back unfortunately to him.
“We had a chance when we were in the box to make something from it with Michail Antonio, and from that, they went up the other end and made it 3-0. I thought the first half wasn’t good, but the second half was much better."
West Ham, in 18th place with 10 points from 14 games, next play Premier League leaders Manchester City on Sunday.