The 58-year-old brought the Greek Superleague into disarray by forcing league chiefs to indefinitely suspend all matches in the wake of the alarming incident on Sunday.
Savvidis was unhappy when a late goal for his side was ruled out for offside and entered the field of play with a firearm, before being restrained as he approached the referee.
Speaking for the first time about the incident, Savvidis said in a statement: "I am very sorry. I clearly had no right to enter the field of play in this fashion. My only aim was to protect tens of thousands of PAOK fans from provocation, riots and human casualties.
"Please believe that I had no intention to engage in a brawl with our opponents or the referees - and obviously did not threaten anybody. Unfortunately, my family and I, as well as my colleagues, have been taken hostage by a totally sick football status quo.
"Despite the non-stop attacks I am facing on all fronts, I fight and I will continue to fight for fair football, equitable refereeing in all encounters and titles being won on the pitch and not in courtrooms."
Savvidis, one of Greece's richest men, is reportedly still on the run after evading local police.