Haaland's two goals for City saw them to a routine 2-0 victory against West Ham at the London Stadium on Sunday.
The pre-season signing from Borussia Dortmund took just 36 minutes to open his account, converting a penalty after being brought down by Hammers goalkeeper Alphonse Areola.
He got his second 19 minutes into the second half as he ran onto a Kevin De Bruyne throughball and slotted past Areola with ease.
West Ham offered little resistance but Haaland was not surprised his new team clicked into gear early, despite the disappointment of losing the Community Shield to Liverpool last week.
"As expected," he said. "We saw the potential already against Bayern [Munich, a 1-0 friendly win], against Liverpool it was a little bit down, but it will come with games.
"It should have been more today but yeah, OK start."
Haaland felt strongly he should have had more than his two goals, as shown by his choice of explicit language.
"I think if you saw the [Ilkay Gundogan] chance before I went off, I should have been there but I f***** it."
When asked to be "steady with the language" by the interviewer, Haaland responded: "S***, sorry."
Pep Guardiola was satisfied with the contribution of his new striker, adding: "Erling scored the two goals, it was important for him, for us, for everyone."
The pace shown by Haaland and the precision of his finish for the second goal evoked comparisons with Thierry Henry on social media, and this apparent likeness even got a mention in Guardiola's interview.
But after hearing the Norwegian come in for criticism after his performance against Liverpool last week, Guardiola was somewhat despairing in his response.
"Of course he has talent but listen, one week ago when he missed the chances [against Liverpool] he was a 'failure'... now, he's going to be Henry or [Cristiano] Ronaldo?
"It takes time, it's the first Premier League game, he's 22 years old, he has a long career [ahead of him] and when he's going to retire, he hopefully spends many years here at Man City but we are [only then] going to analyse what he has done. So be calm."