City are currently fourth in the table after picking up two wins and a draw from their opening three Premier League games.
"We have seven points out of nine and have won the Community Shield against Chelsea so things haven't started too badly," Kompany told the club's official website.
"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.
"Everything was flying in this time last season so we were effectively winning games earlier and making things easier for ourselves.
"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.
"I think this season will be a lot more competitive than last year - just look at the talent that has come into the Premier League during the summer. I don't think any sides around us are weaker - they have all strengthened so getting victories at this stage of the season is the most important thing."