Everton boss Moyes: We'll soon have title contenders nervous
The Toffees recovered from Gaston Ramirez's first goal in English football with a close-range effort from Leon Osman and two strikes from Nikica Jelavic in a 14-minute period before the interval, put them within three points of leaders Chelsea.
"I don't think Everton managers can come in here and say 'Let's avoid relegation' but I think that is always the first route for every club and it still is for Everton," said the Scot, whose side are perennially poor starters.
"The next part is then 'Can we make a European spot and if you are very good can you make the dream spots, the big ones?
"They might be worried if in April time we slip to the top of the league."