• David Moyes believes Everton are much improved
• Fellaini strikes twice but denied hat-trick by woodwork
• Watch all the weekend Premier League highlights (UK only)
David Moyes is not prone to wild claims. He has seen it all before in his 10 years in charge of Everton: the ups, the downs and especially the many false dawns. So when he dares to suggest that his present team may just be his best since he moved to Goodison Park from Preston North End in 2002, it is worth listening to.
Even better than the 2004-05 side, who finished fourth and reached Champions League qualifying? Certainly in style if not quite yet in substance, to judge by the battering they gave Fulham on Saturday only to be denied a deserved victory by a last-minute equaliser.
"I think so," Moyes said, in reply to the best-ever query. "I think it's the best we've played. We're playing really well and we've got a huge amount of confidence. But the team that finished fourth was so consistent. We ground out results, the 1-0s, and we were really good at that, very resilient.
"But this, well, what was it today? Twenty-seven shots on goal. We've been playing that way all season and we've got so many attacking options in the team. We've had a good start compared to our usual starts but top four at the end? I hope so but I just don't know if we will be because of the level you need to get there."
Everton's 2004-05 vintage went on to disappoint. They failed to make the Champions League group stages, losing to Villarreal in qualifying, and also made a swift exit from the consolation prize of competing in the Uefa Cup, going out to Dinamo Bucharest. Another false dawn, perhaps.
But the boys of 2012-13 look fully equipped to emulate, if not better, their predecessors. They lie fourth in the Premier League and, had they not endured a frustrating series of four successive draws, they would be challenging at the top. Steven Gerrard, the Liverpool captain, may have labelled them "long-ball" merchants but there is much more to them than that.
"We've got players who can play and we've got players who can hold the ball and be physical as well," Phil Jagielka, the Everton central defender, said. "We had a lot of possession, we put a lot of passes together and created a lot of chances through neat interchanges. We all play a part in attacking and all play a part in defending. We're fourth, we're still up there, we just need to be more professional in finishing games off."
Fulham went ahead when Tim Howard half-saved Bryan Ruiz's free-kick only for the ball to strike a post and the goalkeeper's shoulder before landing in the net. Overcoming a freak own-goal took time but Everton poured forward relentlessly with the bullish Marouane Fellaini leading the charge. "He was near enough unplayable," Jagielka said.
Fellaini struck twice with fierce shots, also hit an upright and was thwarted by a fine save from Mark Schwarzer. Had his other efforts gone in – and those from several team-mates also – Everton would have secured the win long before Steve Sidwell, a substitute, popped up at the far post to stab in the late equaliser.
Even Martin Jol, the Fulham manager, was impressed. "Everton are very difficult to play against," he said. "They play possession, they overlap, they play one-twos, they play with real purpose. That's a style and that's what I like."
Man of the match Marouane Fellaini (Everton)