The Toffees' hopes of securing Champions League football took a blow on Saturday when they lost 2-0 to Southampton.
Everton are a point behind fourth-placed Arsenal having played a game more, but Howard believes that his side could still overtake the Gunners.
"We still have a chance mathematically so therefore it is not the end," Sportinglife.com quotes him as saying.
"We need to win and play better. There are still six points remaining, if we win and Arsenal drop points we are in the Champions League.
"We are a top team and dropped points but Arsenal can drop points as well."
Everton host Manchester City at Goodison Park on Saturday.