Mark Hughes' side, who defeated Scunthorpe 5-1 on Wednesday night in the Carling Cup, have failed to keep a clean sheet in eight games.
Lescott, a big-money arrival from Everton at the start of the season, acknowledges that statistic is not to the standard expected of an expensively-assembled backline.
Hughes has also paid top price for the likes of Kolo Toure and Wayne Bridge in the past year, and Lescott believes City's inability to record shut-outs could be because defenders are still gelling.
The centre-back said: "I feel I am settling into City's defence with every passing game. The longer you play alongside people the better and easier it gets.
"We haven't kept a clean sheet for a number of games now, so that is the first objective and we are determined to achieve that.
Goalscoring reputation"Everyone in the back four is relatively new to the club, maybe it's because of that. At the moment we are not doing what we are there to do, keep clean sheets, and we must start doing our jobs."
Lescott carved a reputation for scoring goals when at Everton, but it took him nine games to open his account for City and he now wants more.
The 27-year-old scored against Fulham on Sunday before also hitting the back of the net against Scunthorpe.
He said: "I did get a bit of a reputation for goals from set-pieces, so it is nice to have finally scored one for City.
"But the main thing is that we score goals, nobody is really fussed who does. There was no argument about mine on Saturday, everyone knew I got the last touch.
"I just hope to be in the right place at the right time. That's all a defender can do.
"Every time I go up now someone on the bench says, you have to score. They think I should have scored a few more by now."