City beat West Ham United 3-0 win on Tuesday evening to go through with a huge 9-0 aggregate scoreline, and Lescott believes that winning the trophy would give the players the taste for more as they chase down the Quadruple.
"It's very special to start winning trophies and long may it continue," Lescott told Sky Sports News.
"It's a progression thing here, we've been in and around these competitions for the last three or four years.
"We can continue, we're in the right competitions and long may it continue as I say. To get the final, there is never going to be an easy game [waiting for you], but we're there and that's the main thing."
Manchester United entertain Sunderland in the second semi-final on Wednesday evening.