Already trailing 1-0 to Ciaran Clark's deflected shot, the team suffered the setback of losing Danny Rose to a straight red card just five minutes into the second half.
The dismissal didn't disrupt the flow of the game, however, as the 10 men continued to dominate.
Emmanuel Adebayor equalised from the penalty spot in the 61st minute after Sandro was chopped down by Richard Dunne.
Despite a final shot count of 21-4 and corners 19-4 in our favour, we couldn't carve out that one clear-cut chance as Villa sat deep to earn the point that should secure their survival.
"It was always going to be difficult, Villa were scrapping for a point to keep them in the division," said Harry.
"They scored with a shot that took a wicked deflection and you think ‘how’s your luck?’.
"We then got Danny Rose sent off and we’re down to 10 men, 1-0 down, five minutes into the second half.
"At that point, you’re in trouble - but we responded magnificently.
"For the last 40 minutes, we were camped in their half and there was only going to be one winner. We equalised and couldn’t get the second.
"I couldn't ask for more from the players, they put a real shift in. They gave everything."
A share of the spoils at Villa Park and Newcastle's defeat against City means that we hold onto fourth place going into the final weekend of the season.
We're a point ahead of Newcastle and victory over Fullham at the Lane will secure that fourth spot.
Arsenal are a point ahead in third and travel to West Brom - so if we manage to topple Fulham, anything less than an Arsenal win will mean we take third.