The 32-year-old, who kicked off his stint with the Baggies by recording a 1-0 win over Tottenham Hotspur last month, started his career with West Brom's fierce rivals Wolverhampton Wanderers, but he does not believe that there is any ill-feeling directed at him from the fans.
"I think it has helped with the way we've played and getting the result at Spurs was a big thing, but it's nice," Lescott is quoted as saying by The Mirror.
"Before I arrived, I wasn't that concerned about the West Brom fans because I thought if I came here and played well they would hopefully take to me.
"I was more concerned about the Wolves fans and how they would feel now I've come to play for their arch-rivals, but it was a situation that happened."
West Brom take on Manchester United in the Premier League on Monday night.