The Toffees are currently in 17th place in the Premier League table, two points above the relegation zone.
Despite winning just one of their first seven matches, Horne believes that Roberto Martinez's side are more then capable of climbing up the standings in the coming weeks.
"The Premier League table is starting to take some sort of recognisable shape, but it is still very early in the season," he told the Liverpool Echo.
"While the numerical position looks alarming – 17th is just one place above the relegation zone – the reality is that Everton are still just five points behind sixth place and another Europa League qualification place.
"And let's not forget that we've faced Liverpool, Chelsea, Arsenal and Manchester United in our first seven matches of the campaign."
Everton return from the international break on Saturday when they host Aston Villa in the league.