Villa sit third at Christmas, three points behind leaders behind Arsenal.
“I think it was two or three years ago when we were a win away from finishing for Christmas at the top of the table, but we drew to Sheffield United. We had just beaten Arsenal and Man City too,” McGinn told Sky Sports.
“This season has given me so much pleasure because we were written off, sort of down and out. We probably had some doubts ourselves, but the way we have come back from it and gone on this run has been amazing.
“I think we operate at our best when we go under the radar, and the start of the season helped us do that. We slowly climbed the table, but we aren’t actually talking about it (title race).
“We’re in this mode where the games keep coming and we are sneaking a few wins and deserving other wins.
“There’s some world class teams in this league and also teams below us who will be there come the end of the season. We’re not allowed to talk about it, we won’t talk about it and we shouldn’t.”
Asked what has changed about Villa’s form, McGinn joked: “Morgan’s (Rogers) shots were going over the bar! Now they’re dipping a wee bit under the bar, but no, we started really poor and couldn’t find a goal.
“We got closer and closer and have now found our form and some resilience. We have been behind so many times and we come back.
“We’ve got something in there and we have been fighting until the end. The start of the season was quite disruptive because of a few subjects, but then we started to get our top players into form and that’s happening at the minute.”