Haaland scored a hat-trick as champions City ultimately ran out comfortable 5-1 winners over the Londoners but the game turned on a highly contentious incident just before half-time.
Nathan Ake headed City 2-1 ahead but Fulham complained vociferously that Manuel Akanji, stood in an offside position, had attempted to kick the ball on its way past and hindered goalkeeper Bernd Leno.
The protests, both on the field and the touchline, continued long after VAR had ruled the goal should stand and Haaland accepts the visitors had a point.
“I think it was offside as well,” the Norwegian told beIN Sports. “I feel bad for them, I would be fuming after this as well. It must be a horrible feeling for them.”
Prior to that, the game had been rather more sedate with few chances until Julian Alvarez scored a 31st-minute opener that was quickly cancelled out by Tim Ream.
City did not dwell on the incident after the break, moving through the gears with Haaland typically coming to the fore. He finished clinically from an Alvarez pass, fired home a penalty and then turned in a Sergio Gomez cross to claim his seventh City hat-trick in stoppage time.
“I'm back," said Haaland, who scored 52 goals last season. “I am always hungry. It's a new season and I am ready.
“We started a bit sloppy but we ended in a good way. It was important to win - four out of four - and we go into the international break after a really good start.”
City's victory was their second without manager Pep Guardiola on the touchline as he continues his recovery from back surgery, but the Spaniard is expected to return for the trip to West Ham in a fortnight.
“I think he misses us,” said Haaland. “We also miss him sometimes too, so we look forward to having him back.”
Fulham go into the international break without a win since their season-opener at Everton, but veteran defender Ream expects the team to hit back.
The American said: “That's just the nature of the squad, the mentality (manager) Marco (Silva) has instilled in us.
“It's just a shame that we have an international break and it's two weeks between games for some guys. But we'll come back. We'll look at things we can improve upon and we go again when we come back.”