A creditable goalless draw in Copenhagen on Tuesday could not compensate for losing the first leg 2-0 against the Danish champions and it is now 10 years since the Dons made it past the second-round stage.
Alex Ferguson, now of Manchester United, was in charge back then and Aitken is the fourth manager since who has failed to make any impact in Continental competition with the last Scottish club to win a European trophy.
He believes that will change in the seasons ahead, although it would be difficult to emulate Ferguson's success of leading Manchester United to a Cup-Winners' Cup and European Super Cup double in 1983.
Aitken said: "There is a thin line between success and failure at this sort of level and I am confident that we can step across it given the way we played in both games against Brondby.
"Don't forget they have nine internationals in their side and are by far the best team in Denmark, so my players can take a lot of credit from the way they played in the two games.
"Brondby got to the semi- final of this competition last season and have done very well in Europe in the last few years, but we gave as good as we got over the two games.
"It is encouraging that we were able to control long spells of matches against that calibre of opposition and we will see the benefit in the seasons ahead.
"This has merely whetted our appetite to get back into that arena and I know that we can compete in this sort of company. I thought they were fortunate to go through over the two games, and if we had got a break in front of goal I think we would have got the result we were looking for."
Aberdeen now face a tough test back on the domestic front this weekend, with a trip to Parkhead to take on Celtic.
The Frenchman Antoine Kombouare will return in defence after being ineligible for the European game. However, John Inglis may be out for a lengthy spell after being sent home early from the trip with a groin strain.
He will join Paul Bernard and Stephen Glass on the injury list but Scott Booth will be fit for the game in Glasgow despite being taken off in the second half on Tuesday, suffering from fatigue after four games in 14 days following a six-week absence.
Aberdeen were beaten 5-0 the last time they visited Celtic Park, but Aitken is confident of a better result on Saturday after a recent draw at Ibrox.
He said: "This is another big game that the players will be looking forward to and we have to prove that we can match the Old Firm teams regularly.
"We did that effectively at Ibrox by coming back from two goals down to get a draw. The players were disappointed not to win in Denmark but they know how well they played and will be anxious to continue that sort of form at the weekend."