The stage was set for Louis Saha to grab an equaliser against his former club but he struck the woodwork from close range in the third minute of added time.
In the end, Nikica Jelavic’s first-half goal was enough to secure maximum points for the Toffees.
“How did we lose that game?” said Harry at Goodison. “In the second half they didn't come out of their half. It was completely one-way traffic.
“There wasn’t much in it in the first half. They created one or two chances, we created one or two chances and we conceded a goal. It wasn’t as if our keeper had a lot to do.
“In the second half we picked up the pace, got after them and penned them in. We made chances, missed chances, battered them. We just couldn’t get the goal.
“We missed a chance at the end that 99 times out of 100 we would have scored.
“I couldn’t have asked for more than what we did in the second half, to come away from Everton and dominate them like that. It was one of those days.”
We battered away but couldn’t find a goal against a typically steely defensive display from David Moyes’ team.