The Norway international scored the only goal as City beat newly promoted Coventry City 1-0 on Saturday, a result that kept Enzo Maresca's side perfect after three league games following wins over Bournemouth and Crystal Palace.
It is Manchester City's first title race without Pep Guardiola in charge since 2016, following his decision to step down at the end of last season after leading the club to five consecutive titles before Liverpool and then Arsenal ended that dominance.
Speaking to Viaplay, Haaland acknowledged City are not yet the finished article under their new manager, even if their transfer business over the summer has strengthened the squad considerably.
"Arsenal have played together for a long time and have built this up over a longer period, a bit like City had when I first joined," he said. "We're still in a kind of rebuilding phase, but the transfer window has been fantastic, I have to say.
"Well done to the club and the people at the club. First and foremost, they've brought in fantastic footballers, but also great people who fit in really well. So well done to the whole club."
Among City's new arrivals this summer was Enzo Fernández, who completed a club-record-equalling £125m move from Chelsea on deadline day, becoming Maresca's second reunion with a player from his time at Stamford Bridge.
Maresca, who previously managed Leicester to the Championship title before his spell at Chelsea, signed a three-year contract at the Etihad in the close season as City's first appointment of the post-Guardiola era.
Haaland's goal against Coventry continued his remarkable record against newly promoted opposition, having now scored against 23 of the 24 different teams he has faced in the Premier League, with Sunderland the only side to have kept him off the scoresheet.
City will hope his comments about a rebuilding phase prove to be more caution than genuine concern as they look to reclaim the title from Arsenal this season.
City's perfect start stands in contrast to the uncertainty that surrounded the club heading into the season, with question marks over how quickly a new manager could replicate the standards Guardiola set during his nine years in charge. Three wins from three suggests the transition has at least begun smoothly, even if Haaland's comments suggest there remains work to do before City can be considered genuine title favourites once again.