Norway's Erling Haaland opened the scoring in the 29th minute and while Aymen Hussein briefly levelled for Iraq, Haaland put his side back in front before halftime.
Leo Ostigard added a third in the 76th minute and Hussein's late own goal completed the scoring.
Iraq are playing at the World Cup for the first time in 40 years and Arnold said he was encouraged by their performance.
"We put good pressure on Norway," he said. "But a couple of mistakes against players at this level will always punish you. So we need to learn lessons from our mistakes."
The Australian said Norway's second goal, which came from a weak back pass to Iraq goalkeeper Jalal Hassan, was a turning point.
"It really probably hurt the players mentally," said Arnold. "I tried to pick them up and say it's the past, and we've got to get over it."

Despite the defeat, Arnold said Iraq remain firmly in contention to reach the knockout stage.
Norway lead Group I on goal difference, with France also on three points following a 3-1 victory over Senegal.
With the best third-placed sides also able to advance under the World Cup's expanded 48-team format, Arnold said there was no reason to panic.
"We're in a group phase, there's nine points available," he said. "We've got to take all the positives out of today and get ourselves ready for the next game.
"There is still the opportunity for third spot. Three points should be enough to get you through."
Arnold also highlighted the contribution of Hussein, who endured an injury-hit season.
"For him to get through 90 minutes with that energy that he had, of course scoring the goal was fantastic," he said.
With France next up, Arnold called on supporters to stay behind the team.
"Be proud of the players," he said. "Keep supporting the boys and stay happy."
FIFA World Cup 2026
The 2026 World Cup will be held from June 11th to July 19th in the United States, Canada and Mexico. The tournament will feature 48 national teams and will be played in 16 modern stadiums.
Match schedule and times | Group tables | England at the World Cup | Scotland at the World Cup | Team rosters at the World Cup | How to watch the World Cup | Predictions and odds | Which teams could be considered dark horses?
