The owner of the Draft Project, PB Devco, said he was "saddened" by the videos of fans celebrating Scotland's winning goals.
Several videos have been shared on social media from the venue, where fans gathered to watch last night's Scotland match in what appeared to be a marquee.
The clips show fans hugging, singing and standing on tables during the game, after Ryan Christie scored the opener, before Scotland went on to win on penalties.
Owner and founder Stuart Clarkson said: "Having seen the videos I am shocked, disappointed and saddened. This simply is not acceptable and I understand why people are so upset by this.
“While we are proud of our venues and the safe environment they provide, it is clear that in this case we misjudged what was likely to happen. Despite having four additional members of security staff on duty, we were simply unable to contain the outbreak of joy at Scotland’s success.
“I would also like to thank the four Police Scotland officers who attended the venue for around 40 minutes and supported our management and security staff after the first goal was scored. "
Police Scotland confirmed they are investigating the incident but no arrests or FPNs were issued.
Mr Clarkson confirmed he would also be carrying out his own review of the evening.
He added: “We truly hoped and believed we could provide a safe way for customers to enjoy this crucial match and that we could do that within the existing regulations. We took all steps we could to fully comply with those regulations.
“With hindsight it is easy to understand the scenes of sheer, unbridled joy. Unfortunately, in the current pandemic, that is not acceptable and we were unable to prevent or contain what happened.
“I will now be carrying out a thorough review of what went wrong and what steps we have to take to prevent any such repeat incidents. We will also comply fully and assist any reviews or investigations by the police, Aberdeen City Council or the Scottish Government.”
Bars in Aberdeen can currently serve alcohol outdoors until 10pm, but people are only permitted from meeting in groups of up to six from two different households, as long as social distancing is adhered to.
Health chiefs warned of the "deadly consequences" of spreading coronavirus stating "the virus does not rest. It does not take a minute off, much less 90 minutes, extra time and penalties".
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