The Dons face Championship Morton at the national stadium in Glasgow on Saturday 22 October.
And the Premiership club believe their support will be at a "major disadvantage" because of the near 150-mile distance and the 12:15 start.
The other Hampden semi-final, Rangers v Celtic, is at 14:15 on 23 October.
In previous seasons, a number of League Cup semi-finals have been played in Edinburgh, with both Hibernian's Easter Road and Hearts' Tynecastle hosting the ties.
Bus journeys from Aberdeen to Glasgow can take up to three hours.
In a statement on the club website, Aberdeen said: "Our stated preference was that the game took place at a more reasonable time on the Saturday at a venue that would ensure a capacity attendance.
"It is from an attendance perspective very regrettable that the game kicks off at 12.15pm, which is a major disadvantage to our fantastic travelling support in particular for games such as these.
"Regarding the choice of venue we understand and accept that it is for all clubs to indicate the crowd they anticipate taking and Hampden Park was chosen on this basis.
"We accept that the majority of our supporters would have had to travel for at least a couple of hours to attend this fixture at any suitable venue, but are disappointed as we feel that this outcome has a very negative impact on what should be a great day out and experience for all supporters."
Aberdeen say it is "very regrettable" their Scottish League Cup semi-final with Greenock Morton has been given a lunchtime kick-off.