The Toffees head into Sunday's game on the back of a seven-game unbeaten run and Moyes will undoubtedly be looking for an improvement on last year's opening day defeat.
“It was a terrible period," Moyes told The Sunday Express.
"I was hoping to get to the end of the transfer window without losing any of my players and hoping everything would calm down.
“Manchester City wanted Joleon Lescott and that game solidified it for me. I had probably been trying to fight something I maybe shouldn’t have."
Meanwhile Arsenal manager Arsene Wenger has been critical of some opposition players for being overly physical, but in Wednesday's win over Wolves it was Arsenal who were criticised.
Moyes observed: “Maybe they are just giving back what they think they have been getting.
“But we have to have tackling in the game and we must have players who are committed.
“Supporters who have paid good money don’t want to see folk tip-tapping around.”
The fact that Wenger was criticising one moment and being criticised the next shows that football is unpredictable, something Moyes believes is true of football management.
“In football management, every day you come into work your job is not secure,” he said.
“I feel that if I don’t work hard every week I could be in jeopardy myself.
“In horse racing terms, I have to be out of the saddle all the time, whip ready.
"I don’t think at Everton we are ever able to canter, We always have to stand up in the saddle and go for it.”
The Everton manager is the Premier League's third-longest serving manager, behind Wenger and Manchester United's Sir Alex Ferguson, after spending nine years with the club.