A trio of late tries on Sunday lent the scoreboard a distinctly flattering look for the visitors, who had been wholly outclassed either side of the interval and remain pointless with three games gone.
"I'm really happy with the first 60 minutes but we need to be an 80-minute team," former Parramatta boss Arthur said.
"We just tried to play too cute and too pretty in the last 20 minutes instead of playing tough like we had in the first 60.
"We did all right to get to 38 points and I don't know why we got bored with that."
Leeds laboured through the first 20 minutes before Jake Connor's opener sparked a period of dominance in which the hosts ruthlessly punished their opponents' errors.
But, after seven players scored tries to put the result beyond doubt, the home side bizarrely let the visitors off the hook, much to Arthur's annoyance.
"The positive thing is that we didn't get any injuries out of the game and we can learn the lesson of the last 20 minutes without it having cost us two points," added Arthur.
"The game was in the bag but Wigan wouldn't do that, would they? We're only in round three and we're miles away from where I want to get to and where this team wants to be."
Former Rhinos hero Danny McGuire endured a painful return as Castleford head coach but tried to find some positives with his side still searching for their first points of the season.
"I was proud of the way we kept battling to the end but I just think we're lacking any kind of consistency with our actions at the moment," he said.
"There were some positive signs but there was some real lack of discipline, errors and poor skill, and Leeds took advantage."
McGuire, who won eight grand finals during his glittering playing career at Headingley, warned Tigers fans it will take some time before his efforts are reflected in results.
"It was never going to be a straight road this year, there were always going to be some curves and bumps in it," said McGuire.
"We can't feel sorry for ourselves, and we've got to work to get better as a group."
