Bendtner and his Sunderland team-mate Lee Cattermole were arrested on suspicion of causing criminal damage to parked cars near Newcastle United's St James' Park stadium.
The 23-year-old, who is on loan from Arsenal, was also involved in a recent incident in a Copenhagen pizzeria when his credit card was rejected.
Bendtner released a statement to the Ekstra Bladet newspaper in Copenhagen in which he said he was "sorry that I have let so many people down" and promised to end the "extracurricular activities" that have got him in trouble.
"Dear friends, fans, Sunderland and family," he said. "The past couple of weeks have seen me involved in several incidents that have attracted much negative attention from the media."
He explained: "After the friendly international against Finland [on November 15] I was part of an unfortunate incident at the team hotel where I more or less was portrayed as a violent character.
"Anybody who knows me can testify that I am not. Police in the end decided not to press charges.
"In connection with a birthday celebration with my girlfriend I was part of an incident at a pizzeria in downtown Copenhagen where my credit card got rejected. I bet you all know the feeling but in this case it was also described in the media.
"The latest incident involves two of my team-mates and me who were picked up by polite and friendly English policemen as CCTV footage allegedly shows us in the process of damaging parked cars after a night out on the town.
"This case now has to make its way through the British system of justice and a verdict is expected by February next year. In connection with all these incidents I have to make one thing very, very clear.
"I am extremely sorry for all of this. I apologise sincerely that I have allowed myself to get involved in things that are interpreted in such dramatic fashion. I fully assume responsibility for not distancing myself from these incidents before they got out of hand.
"The error is mine alone and I am sorry that I have let so many people down. Basically, I am a normal guy with an extraordinary job."
He added: "My primary objective right now is to get rid of my injury and get back into full fitness for Sunderland and Denmark. I hope you will understand that I now promise to concentrate fully on football and only football. My focus has to be here - and not anywhere else."
