Instead, Solbakken's side will take on Bayer Leverkusen over two legs for a spot in the Champions League group stage and although the Norwegian coach conceded Copenhagen will need "a little luck" to overcome the Bundesliga club, he claimed he was "relatively content" with the draw.
Having finished second in the Danish Superliga last season, Copenhagen have been forced to try and qualify through the 'League Route' of Champions League qualifying, rather than the 'Champions Route' that does not include the likes of Arsenal, Napoli or Porto.
In contrast, Danish champions AaB drew APOEL from Cyprus in the play-off round.
"We are relatively content," Solbakken told Copenhagen's website.
"No matter what we would have met a class opponent, where we would be definite underdogs.
"We really wanted to avoid Napoli and Arsenal, who have the most experience in this [group].
"Leverkusen are an experienced team, who have played a lot of Champions League. They are always in the top three or four in Germany.
"But now we will study them and then I might regret what I have said."
Solbakken claimed he has an idea what to expect from Leverkusen on August 19 and 27.
Leverkusen have a new coach this season - former Red Bull Salzburg boss Roger Schmidt - and Solbakken is well aware of the German tactician's playing style.
"Salzburg played in an aggressive way, pressing all over the pitch," the 46-year-old said.
"They crushed Ajax for example [in last season's UEFA Europa League] and had an enormous capacity to run. It will surely be the same at Leverkusen but we'll found out about that quickly."
Copenhagen are looking to qualify for the Champions League group stage for the first time since 2013-14 when they finished bottom behind Real Madrid, Galatasaray and Juventus.
The Danish capital club's best Champions League campaign was in 2010-11 when they reached the round of 16 ahead of Rubin Kazan and Panathinaikos.
Copenhagen drew at home with group winners and eventual champions Barcelona that season.
