But while that may give him short-term gratification, which has been in short supply for him in clashes against their near-neighbours, what he really craves is success on a bigger scale. The red half of the city may have ended their six-year trophy drought with a Carling Cup triumph last month, but Moyes is still waiting for his first piece of silverware.
"I'm the first person to say I've not won anything so I don't need other people to tell me," said Moyes, whose side are one match away from a Wembley FA Cup semi-final. "I am ambitious and still driven to try to succeed and as long as I have got that I will try to do it."
He continued: "I don't think anyone will have a greater ambition than me. I am desperate to win trophies and cups but I'd like that to be at Everton and my focus and loyalty is to make sure I succeed.
"I am really lucky that I am in this job and what I want to do is get the supporters to Wembley and touching silverware as much as I can. It has been tough to give the fans success over the years but I hope the supporters see there has been a stability.
"There is a level to what we can do. There always has to be an Everton Football Club and we have not overspent in the main, kept things right and because of that we have got a pretty good Premier League team. We'd love it to be better and winning the Premier League but at this present moment we can't do that."
The Toffees make the short trip to Anfield on the back of a nine-match unbeaten run in all competitions while the home side's Carling Cup success is sandwiched between three successive league defeats, but Moyes feels the form of the two clubs will count for little on the evening.
He said: "A lot of the years I have gone into the game and Liverpool have been the form team, and folk have said: 'Who knows in derbies'. You never do know."
Victory at Anfield is something the Scot is yet to achieve in his tenure with Everton's last triumph there coming in 1999.
Asked if he would be happy simply not to lose the game, Moyes said: "Over the years, I think it would have been a great result for any team to go and do that, because Anfield has been a hard place to go. We will go to Anfield and try to win, and then if you can't do that, the next thing you want to do is try to get a draw."
Source: PA
Source: PA