Moyes watched on against his former side as Everton's early dominance was rewarded in the 18th minute through Michael Keane's header beyond the grasp of Alphonse Areola. 

Indeed, Keane's opener was Everton's 361st headed goal in the Premier League – no team has scored more in the competition's history (level with Manchester United).

Iliman Ndiaye and Beto had earlier tested visiting goalkeeper Areola before Kiernan Dewsbury-Hall tried his luck as the Toffees entered the break in the ascendancy. 

But apart from Idrissa Gueye's speculative effort four minutes after the restart, Everton was unable to generate any clear-cut chances, with West Ham improving from there on. 

The Hammers came close to finding an equaliser through Crysencio Summerville after a mistake from Jake O'Brien, but Jordan Pickford was on hand to deny the Dutchman. 

However, West Ham's persistence was rewarded in the 65th minute through Jarrod Bowen's fine equaliser, which marked the first goal of the Nuno Espirito Santo era. 

Though James Garner's stinging strike was repelled by Areola late on, Everton needed a last-ditch tackle from James Tarkowski to deny Bowen at the other end. 

"We played some decent stuff at times, we got a goal but we couldn't get a second one, which would have been all important," Moyes said.

"We did a lot of good things, but we just couldn't quite craft a chance to get a second goal. Once we didn't get it, West Ham grew in confidence and belief that they could get something themselves, which they did.

"Some good things and some not so good things but West Ham have talented players so it was always going to be a tough game for us." 

Everton's profligacy in the final third was not through a lack of effort, with Jack Grealish creating four chances for his team-mates against West Ham. 

No player has created more chances than the Manchester City loanee in the Premier League this season (17), but they were unable to find the finishing touch throughout. 

Everton is without a win in their last four games in all competitions, after its derby-day defeat to Liverpool and Carabao Cup exit to Wolves last week. 

It was Everton's second consecutive draw at Hill Dickinson Stadium, with Bowen's strike the first time it has conceded in competitive action at its new stadium since its switch from Goodison Park. 

Moyes's men welcome unbeaten Crystal Palace to Merseyside, and while still getting used to their new surroundings, the Everton boss expressed the need for improvements.

"It's certainly one we are more familiar with, but we want to win. Our record here at the moment has been good enough, we want to keep it going," Moyes said.

"We started the season well. We want to raise expectations, but we can't forget that we have a long journey to go, and we are just at the start of it."