Calvert-Lewin's clinical 24th-minute strike proved the difference as Everton recorded an 11th Premier League away win of the campaign.
“It was a tough shift," said Calvert-Lewin, who sunk to his knees when the final whistle sounded after a tireless and unselfish centre-forward performance.
“It was about determination, hard work and sticking together. That's what got us the three points.
“We went 1-0 up and we had a few chances. But we mainly sat behind the ball and dug in and worked hard. It wasn't pretty but I think, for the effort we put in, we deserved the three points.
“For the goal, we knew we'd be able to expose them in behind. So, when Richy showed for the ball to feet, I've just timed my run [in behind the West Ham defence] perfectly – we've been working on that in training – and Godders has put a perfect weight of pass in. Then it was just a touch and finish."