The Merseyside outfit are four points adrift of the final Champions League qualification spot, which is currently being occupied by Chelsea.
"We are right there, we are breathing heavy down a few people's necks," Sky Sports News quotes Howard as saying.
"We need a little bit of luck for those around us to drop points. But maybe we are in a position to make our own luck. People say it's daunting but it's an opportunity for us."
The Toffees have eight games remaining to grab enough points to edge out Chelsea, Arsenal or Tottenham Hotspur in the top four.