Remi Garde's side beat Norwich City 2-0 on Saturday.
The Villans are widely expected to be one of the relegated sides come the end of the season, having spent nearly the whole campaign at the bottom of the table.
Recent weeks have seen some improvement for them though, having managed eight points from their last five games in the Premier League.
The latest of those was a 2-0 win over Norwich City at the weekend to leave them eight points from safety and Lescott says they have nothing lose in trying to mount an unlikely escape from relegation.
“Everyone has written us off, so we've got nothing to lose,” he told avfc.co.uk. "If we go down everyone says: 'Well, we knew that in January or February.'
"But we've got a great fighting spirit and we believe that if we show that kind of desire and attitude in every game then we'll make a real fight of it.”
If Villa are to stand any chance of staying up this season, they will have to take all three points from some difficult upcoming fixtures.
Rather than taking on teams around them, they now face a run of tough fixtures, with four of their next six games coming against sides in the top ten.
That is sure to make things much more difficult for them, with those teams, such as Everton, Liverpool, Tottenham Hotspur and Manchester City, all eyeing a strong end to the season to secure a place in Europe next year.