FC Copenhagen managed to draw 0-0 against Chelsea on Wednesday, but lost the first leg 2-0 at home in Copenhagen.
Solbakken told Uefa.com: “I can only congratulate Chelsea on going on in this tournament.
“They were the better team overall, and they also did well tonight, but I am proud of what we have achieved in this competition. We have played eight games, and we have played well in seven of them.”
He added: “The game at Parken [the first leg against Chelsea] was the performance we were not content with, but in general we have to realise that we were knocked out by a better team.
“However, it was a magnificent performance to get a goalless draw here. Our central defence was extremely strong, our goalkeeper did well and in general our display was very satisfying.”
