Lescott told the club's official website: "It was a massive result. We knew it extra special today and our main thing was to keep it as close as possible for as long as possible.
"When you do that away from home then there's more pressure on the home team as the game comes to a close. First half, we were very pleased to go in at 0-0 and we knew we had to concentrate equally as much in the second half.
"Then, if you've got people putting in quality like Chris Brunt then you've just got to get on the end of it."
West Brom are 16th in the Premier League after collecting five points from their opening five games of the season.