The Reds, who have largely disappointed in their domestic campaign, finished top of Group E, winning four and drawing one of their six matches to secure a home qualifier in the last 16 for the second time in three years.
Despite being thought of as the least likely of the three Australian teams to qualify, Adelaide are now the country's sole representative heading into tomorrow's [Tuesday] sudden-death encounter.
And Galekovic is happy for the Reds to remain underdogs at the Hindmarsh Stadium.
"No-one has really rated us since day one and we weren't even meant to get to this stage, so considering that you could probably say that the pressure is off us but as a playing group we do want to qualify for the quarter finals," Galekovic told www.footballaustralia.com.au.
"That was our aim from day one, we've been to the knockout stage three times now, been successful once and unlucky when we lost in extra time against Jeonbuk in 2010, so we do want to progress, that's our aim as a playing group, others might not see that but we really do want to go as far as we can.
"There's one more game to go and I can guarantee we will give our all."
Attempting to stop them is a Nagoya side that finished runners-up to Korean club Seongnam Ilhwa in Group G.
With Qantas Socceroos striker Josh Kennedy and veteran former Japan international Keiji Tamada in their ranks, Galekovic is aware Dragan Stojkovic's men are a side that cannot be taken lightly.
"Any time you come up against a Japanese opponent they are going to be quality and Nagoya is one of those," Galekovic added. "They've obviously got Josh (Kennedy) up front, another striker in (Keiji) Tamada who is scoring goals as well so it's not just one guy we have to watch out for, there are a number of them so we'll be aware."
"We know they're a quality team and on paper they might be a better team than us, but as a group we've shown this year in the ACL that we can match it against the best and hopefully come tomorrow [Tuesday] we can."
Also tomorrow [Tuesday], Seongnam IIhwa Chunma of Korea will host Bunyodkor, the Uzbekistan side that finished runners-up to Adelaide in the group stage.
On Wednesday, Group F winners Ulsan Hyundai from Korea will welcome Japanese outfit Kashiwa Reysol, while FC Tokyo will travel to China to face Group H winners Guangzhou Evergrande.