The Toffees looked to have dropped out of the race to play in next season's elite European competition after drawing far too many games, coupled with back-to-back defeats in February.
But Saturday's 1-0 success against Stoke made it a perfect three from three in March and they now sit in sixth place in the top-flight standings with 51 points from 30 games played.
Arsenal are two points and one place better off with Chelsea another couple of points to the good but, with eight games to go, Howard feels it is all still to play for.
"We are right there, we are breathing heavy down a few people's necks," 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."
Punters looking to use a free bet might fancy the Merseysiders to bridge the gap and finish in the top four and they are next in action against one of their rivals for Europe, Tottenham, on March 7.