The Toffees are currently in fifth place in the Premier League table following Saturday’s 1-1 draw at Stoke City.
That stalemate was Everton’s seventh in their last 10 top-flight games, with Moyes’ men only managing two wins in their last 10 Premier League outings.
But despite the recent dip in form, the Everton boss is still hopeful his side can keep up with the likes of Tottenham Hotspur and Arsenal as the season continues.
“We know that we have not got the strongest squad. We are certainly short. We don’t have an awful lot,” said Moyes.
“We’ll do everything we can to finish in the top four. I don’t know, when it comes to it, if we will actually have enough. I couldn’t be sure if we will.
“But I am not going to talk us down. We are up there because we have played well at the start of the season. Realistically, will it happen? I don’t know. But I want us to try and keep pushing and pushing and try to get a position in European football if we can next year.
“I think the middle pack is quite strong. I don’t think it would take too much for a team to win three games in a row to be right in the mix. I don’t know if we will be there but I know that the competition is quite hot, that’s for sure.”
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