Midfielder Lee Carsley returned to full training for the first time this season claiming Everton can still match last term's fourth-placed finish.
The Irish international has not played since sustaining a bad knee injury in a pre-season game with Fenerbahce.
He returns with Everton bottom of the Premiership for the first time in eight years and on the brink of their second European exit of the season.
Carsley believes Everton will soon be surging up the table, saying: "We are more than capable of finishing where we did last season, there is a long way to go yet.
"We have to stick together and be strong and we know the next few games will be very tough.
"If we can just play as well as we have been doing on occasions, I am sure that things will turn for us."
Everton were knocked out of the Champions League at the third qualifying stage by Villarreal a month ago, and they are now expected to exit the UEFA Cup on Thursday when Dinamo Bucharest bring a 5-1 lead to Goodison Park for the second leg of their first-round tie.
Everton follow that game with three away Premiership matches against Manchester City, Tottenham and Birmingham and a home match with Chelsea.
Confidence has been affected by the poor sequence of results, and the club will lose out financially if Dinamo complete the job they began so well a fortnight ago.
But Carsley is determined to rally his team-mates, adding: "We still have a fantastic squad and we have been very unlucky with injuries.
"I am sure once we get our strongest team together and have a fully fit squad to choose from, things will not be a problem. There is certainly no 'panic stations' at Everton."
There have also been positive words from chief executive Keith Wyness, who has seen only 15,000 tickets sold so far for the Bucharest game.
He said: "There is a chance we can turn this around. We know it is a slim chance but we all firmly believe it can be done.
"But there will be less chance of it coming off if we don't have a noisy crowd cheering us on."
Moyes needs his injured players back in action quickly to halt the worrying slide, and Danish defender Per Kroldrup is also training again after a hernia operation.
