The result further compounded Liverpool’s recent woes, leaving Arne Slot’s team with just one win and six defeats out of their last seven league matches.
The Gunners secured three points to top the league table.
The tough clash between the English and Portuguese sides saw Forest win through two spot kicks, the first coming from a handball incident involving Porto defender Bednarek.
They did at least score their first goals of the season through Abdoulaye Doucoure and Arnaut Danjuma, but with a single point from four games, it has been a frustrating start to the campaign.
Kompany will take over from Mike Jackson who replaced Sean Dyche in April but could not rescue the clube from relegation.
The pressure at the bottom of the table has now shifted to 18th-placed Everton and Leeds, who dropped to 17th following Burnley’s win.
The surprise decision brings to an end a reign in which Dyche twice gained promotion from the Championship and regularly overachieved on a small budget.
