The Korean side came from behind to lead late in the Group G clash at Docklands Stadium, before conceding to settle for a share of the spoils.
Having beaten Yokohama F Marinos on matchday one, Jeonbuk now have four points from their first two outings in the 2014 edition of the elite club competition, as they aim to go one better than last season's beaten finalists FC Seoul.
"Obviously our ambition and our goal of this Asian Champions League is winning the championship," he said.
"It is a very tough schedule for us. We have to play three games in six days and we have a very busy schedule before the World Cup starts. So it's very important to play well in the group stage to qualify for the round of 16."
Having opened the K-League season with a win at home to Busan I'Park and with another big game away to Incheon coming up this weekend, Choi, much like his opposite number Kevin Muscat, said juggling his team's dual commitments was a priority.
"It was a very tough game for us," he said.
"I was concerned with the problem of our fitness level.
"We played on Saturday. When we left our (training base), the total journey was 22 or 23 hours to arrive in Melbourne. So unfortunately the recovery (from Saturday's game) was not completed. My players did their best, played well and I accept the result."
Choi also backed Melbourne Victory to cause Yokohama problems at AAMI Park next week if the hosts can replicate the level of performance which saw Muscat's side earn a 2-0 lead away to Guangzhou Evergrande on matchday one.
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