The relegated outfit conceded an early goal to the Gunners before a late flourish from Olivier Giroud, who finished with a hat-trick, and an own-goal from Mark Bunn saw them end the season with another heavy defeat.
However, Black felt the scoreline flattered Arsenal as he believes his players performed to a decent level throughout the contest.
"I thought we contained them for a good 80 minutes," he said.
"We had a couple of enforced changes before the game, we asked two midfielders to play (in defence) and I thought they behaved admirably, I thought they worked extremely hard.
"Having conceded a goal very early on, you fear the worst but we stuck at it and not only that in the second half there was a little period where I thought we put Arsenal on the back foot.
"The players deserve a lot of credit and it is a 4-0 defeat but you take that on the chin, but I thought it was harsh the 4-0."
Villa finished the campaign in 20th position on the Premier League table with just three wins from their 38 matches for a meagre total of 17 points.
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