Everton’s defeat by Liverpool on Sunday hit the club hard on two fronts in particular.

First, and most obviously, it left the Goodison Park club licking their wounds, having come out second-best in a battle for local supremacy that they had dominated for long spells. Second, and perhaps more seriously, it left them languishing above the relegation zone amid a desperate run of form.

But a further spin-off was that Liverpool’s emergence from the crisis that had threatened to engulf their season has brought their neighbours’ struggle into sharper perspective. No one at Everton is yet willing to admit that they are involved in a fight for survival, but there is an acknowledgement that results need to pick up almost immediately or else a battle against relegation could await them.

“We didn’t even consider we might get dragged into a relegation fight,” Steven Pienaar, the Everton midfield player, said. “You don’t think about it like that. Sometimes you can go on a bad run, and that’s what is happening with us now. But there are still plenty of games to go. It’s nothing to panic about.”

There was much about Everton’s display against Liverpool that will have satisfied David Moyes, their manager. The team spirit that had helped to propel them to last season’s FA Cup Final was once again evident and their performance was a marked improvement on their previous outing, a 3-2 defeat by Hull. Once again, though, the result went against them and they are now only three points above the drop zone, having won once in their past eight league games.

Tim Cahill, the acting captain, was even more emphatic in his verdict than his South African team-mate, conceding that Everton’s worries are mounting and that an upsurge in form is needed to alleviate them. But the Australia midfield player has seen nothing, even in an injury-ravaged campaign, to shake his belief that the club are too good not to pull away from trouble.

“We’re in a lot of trouble,” Cahill said. “The only way we can get out of it is by playing and working our way out of it. We are too good to be in this position. It’s just one of those things and nothing’s going to fix it except our mental attitude as individuals and as a team. I’m a lot more positive, though — we played better football and had a much better attitude.”

Few at Goodison Park on Sunday would argue with that assessment. Everton controlled the game against Liverpool and will be cursing a combination of ill fortune and poor finishing for their failure to come away with at least a draw. With domestic victories proving so hard to come by, Pienaar is hoping that a European assignment will provide the springboard for a much needed improved run of form, with Everton set to face AEK Athens in a Europa League tie in Greece tomorrow night.

“This result [against Liverpool] doesn’t help our position in the table at all,” Pienaar said. “But in football you have a chance to right things quickly, and on Wednesday we have a chance to make things right.”

• Glen Johnson believes that Liverpool’s 2-0 win over Everton in the 212th Merseyside derby match could kick-start their stuttering season. Johnson, who enjoyed a solid game at right back against Everton, singled out Javier Mascherano’s shot, which went in off Joseph Yobo, as a sign that their fortunes are about to improve (Tony Barrett writes).

“You maybe can’t read all that much into just one goal, but it’s the first time we’ve had a little bit of luck in a while,” Johnson said. “The lads are working as hard as they can all week, so maybe they deserve that luck. Now it’s up to us to make the most of it. This result might end up being the turning point of our season.”