The Reds custodian has described his side's achievement as "massive", with United set to host their Round of 16 match against Nagoya Grampus on May 29
United brushed off a disappointing 2011-12 A-League season to finish top of Group E of the ACL, clinching a home Round of 16 final courtesy of a 2-0 win over Gamba Osaka on Wednesday.
The victory crowned a superb group stage for the Reds, in which they picked up crucial wins away to Uzbek champions Bunyodkor and Gamba among their four victories.
Adelaide now face Gamba's J-League rivals Nagoya Grampus at Hindmarsh Stadium on May 29 in a one-off match, with the winners to progress to the quarter finals.
"It's massive. We know how big it is but when you think about it, it's almost only just the start," Galekovic said.
"Now we've got to worry about the Round of 16 and then hopefully the quarters, semis and the final, and I think we can do what we did in 2008 [when the Reds reached the decider, only to be beaten by Gamba].
"I believed we could get through and I think a lot of the boys did. Obviously you get some of the outside people thinking how much we struggled in the A-League and that we would struggle in the ACL, but it happened last time as well. We believed we could do it and now we've done it."
On the Gamba win, Adelaide assistant coach Luciano Trani added: "We showed our discipline and, at times, attacking football, and that is something we always wanted to continue to play. Tonight the goals we scored were from some good passages of play.
"We have players who are good enough to play patiently. There were times we could have forced it. The game was a tense type of affair for the first 20 minutes, and we needed to make sure we made good decisions.
"But at the same time we didn't want to force situations, where in the end we didn't create those chances because there were none. So the patience in our play became, in the end, what gave us the result."