City conceded the fewest goals in the Premier League last term with just 29 but have shipped five in three matches so far in 2012-13 and is currently fourth in the table, managing to secure a draw against Liverpool only thanks to a glaring late error from Reds defender Martin Skrtel.
The club captain, however, insists that his team have got off to a good start but that their opponents are proving more challenging than last year.
He told the club's official website: "We have seven points out of nine and have won the Community Shield against Chelsea so things haven’t started too badly.
"We have had some really good periods in games, but there are areas we need to work a bit harder on. We're not dismantling teams at present like we were at this stage last season.
"We generally give very few chances away, but when we have so far in the opening weeks, we've been unlucky because teams have punished us, though I think we have defended well overall."
|"If I had one message for the team, it would be: 'Well done guys, we've proved we have plenty of character'"
- Vincent Kompany
The Belgium international center back also pointed out that the team's attack is yet to come into form, and that midfielder Gareth Barry is still out injured.
He added: "Gareth is an incredible player and we've missed him and we will obviously welcome him back, but while we've conceded goals this season, we proved last season that we did well because offensively we scored so many goals.
"If you look at the games in December, January and February, that's the time when we've carried the team in the past and I'm sure we will do the same again if we have to.
"So I'm happy with things so far. If I had one message for the team, it would be: 'Well done guys, we've always battled hard and shown how strong we are as a team and proved we have plenty of character'.
"If we can win games when we are supposedly not at our best, what will happen if we did hit top form? If that really is the case, then the best is yet to come."