The Kiwis' execution was also lacking due to the fact several players, including the side's three playmakers - Leuluai, Shaun Johnson and Issac Luke - had not played for six weeks since the Warriors last game on September 4.
Australia also had several players who weren't involved in the NRL finals but six of their starting side enjoyed a hit-out for the Prime Minister's XIII against Papua New Guinea three weeks before arriving in Perth.
England will get their chance to work out some rust when they play a warm-up game against France in Avignon tomorrow and Leuluai says the Kiwis could have benefited from playing a similar fixture themselves.
"In retrospect, yeah, most probably," he said. "Especially the guys that hadn't played for a while, it most probably would have been a lot better.
"It (cohesion) will improve. A number of us had not played in a number of weeks and that showed. I definitely felt a bit rusty and sometimes there's no ways around that."
The Kiwis realise the enormity of the task they face having not beaten England at home since 2005 and with last year's end-of-season 2-1 series defeat still fresh in their minds.
"We haven't performed the best over there," said Leuluai. "We definitely know now not to underestimate them and they've got a new coach now in Wayne Bennett, who's a decent coach, so it's going to be a really tough challenge."
Kiwis captain Jesse Bromwich believes England are capable of winning the tournament, and says the size of the host nation's forwards and the dour Northern Hemisphere conditions have them anticipating another torrid physical battle.
"I think so, after last year's three game series," said Bromwich. "It was tough but we're not going to lie down and let them walk through us.
"We're going to putting out best foot forward and hopefully they don't win the tournament.
"With big Sam Burgess leading them this year they're going to be very physical again. I'd expect definitely a tough match and it's going to be wet over there so it will be even more of a forward battle."
The Kiwis begin their Four Nations defence against England in Huddersfield next Sunday (NZT) before a rematch with Australia at Coventry on November 6 and an appointment with Scotland at Workington on November 12. The tournament's final will be at Anfield in Liverpool on November 21.