David Moyes and Jack Grealish were left frustrated by some of the referee's decisions during Everton's 2-1 derby defeat to Liverpool on Saturday.

First-half goals from Ryan Gravenberch and Hugo Ekitike settled the game for Liverpool, who held on in the second half after Idrissa Gueye had pulled one back for Everton before the hour mark.

Moyes remains winless in all 21 of his Premier League games at Anfield (D6 L15) – the most games any manager has ever taken charge of at a ground in the competition without winning.

The Toffees have won just 11 of their 67 matches against Liverpool in the Premier League (D26 L30), a win rate of 16%.

However, Moyes felt Everton did not deserve to walk away from Anfield empty-handed, questioning some of the officials' decisions, including the booking for Kiernan Dewsbury-Hall for a quickly taken free-kick in the second half.

"We were much closer. The performance in the second half warranted us to get something, but we gave too much in the first half," Moyes told BBC Match of the Day.

"The boys never gave up and showed a great deal of resilience.

"The bigger thing is the game seemed to be controlled by the referee; we couldn't start anything quickly. We couldn't play.

"I have had played plenty of games where teams have taken quick free-kicks and it hasn't been the referee's whistle.

"He never allowed us to get the game underway fast when we wanted to. I found it strange there was only three minutes [of stoppage time]. If Liverpool were 2-0 down, I'm not sure if three minutes would have been put up."

Everton finished the game with nine shots, two of which were on target, accumulating 0.6 expected goals (xG) to Liverpool's 0.94 from 11 attempts.

Grealish, who has impressed since making the switch to Everton on loan over the summer, was at the forefront of their attempted fightback, creating three chances and putting in five crosses – both game highs.

He echoed Moyes' frustration and hailed Everton's improvement in the second half.

"It [the Merseyside derby] was what I expected, coming here it was hostile, faster," Grealish, who was booked after the full-time whistle for his protests to the referee, told TNT Sports.

"I don't think we played well at all, really, in the first half, and then we lost the game. Frustrating because if we had played like we did in the second half, pressed like that from the start, it would have been a different game. In the end, we couldn't get that last goal.

"It was a bit frustrating in the second half. They're trying to slow the game down at times, and I've never seen a player in my whole life get booked for taking a quick free-kick. Even the stoppage time, three minutes and one minute, I've never seen that.

"I get that sometimes you want to let the game go. I completely get that, but you can't not give something for us, and then two seconds later, one of their defenders gets touched in the back, and they go down, and then he gives it. You can't do that."

Grealish also credited Moyes for his reinvigorated performances since moving to Everton, claiming he has found his spark again.

"I've come here, and he's [Moyes] been so, so good with me," he added. "I love playing for him.

"As soon as I spoke to him on holiday, I knew I wanted to come and play for him. I thank him for giving me my love back and waking up on a match day and wanting to smile and play again, and the fans, but I want to come here and make a difference in games like today.

"It wasn't meant to be, but we've got games coming up, and we want to get back on track."