Saturday's win over Stoke City means the Blues are just four points behind current fourth-placed side Chelsea and they remain in the hunt for Champions League football next season.
Goalkeeper Howard, who returned to the side at the weekend following a spell out injured, admits Everton will need other teams to drop points between now and the end of the campaign but the American says they are ready to take advantage.
He said: "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."