Solbakken's side took the lead after 15 minutes through Nicolai Jorgensen, but thereafter Copenhagen were indebted to an outstanding display from goalkeeper Johan Wiland for claiming a point from their UEFA Champions League opener.
Wiland was beaten 10 minutes into the second half by Fabio Quagliarella, but as the game progressed he pulled off a number of fine saves to ensure the opening Group B encounter ended level.
After the match, Solbakken was frank in his assessment of his side's performance.
"Our first half was next to perfect," he said.
"As the second half progressed we got tired, the distance between the players got bigger and we started to make the kind of mistakes you make as the result of being tired and missing control.
"However, we had a great goalkeeper and our heart was in it all the way."
Captain Lars Jacobsen was happy to admit that Copenhagen had enjoyed their fair share of luck during the game.
"I think everyone could see that we were not exactly unlucky," he said.
"Our first half was OK, while we got under heavy pressure in the second. However, we had a fantastic goalkeeper, and that is what you need in a match like this.
"We realise that the three away matches will be tougher than this one was, but this draw gives our confidence a tremendous boost."
Former Juventus defender Olof Mellberg, now of Copenhagen, was delighted to claim a point against his old club.
"We have got a point against one of the best teams in the world, and we should be content with our performance and with the result," he said.
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