Villa won through an early Anwar El Ghazi goal.
McGinn said, "Not many people would have fancied us without Jack [Grealish]. Leeds are really fit, they make you work hard for the goal. We got it early today and showed lots of character.
"They have a lot of threat but it leaves some weaknesses at the back. We maybe sat back a bit too much, but we'll take the three points. It's massive.
"We've got the chance [to finish in the top six] but there are some top teams in there. We'll just take it game by game, starting on Wednesday [at Sheffield United] – that'll be a tough game as well."