"I love this club and was so disappointed to lose against Manchester United last (Tuesday) night," the Dane, who came on as a second-half substitute, said in a statement on Arsenal's website.
"Reaching a Champions League final is one of my biggest dreams and getting knocked out was a massive blow," he said after Tuesday's 3-1 loss and 4-1 aggregate defeat.
"However, no matter how disappointed I was, it does not excuse my behaviour later in the evening. I may be young but my actions were a poor error of judgement and something I deeply regret. I want to apologise to the club and the fans for letting them and myself down."
The 21-year-old Danish international has struggled to win over the club's fans this season despite scoring 14 goals in all competitions.
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