During the second half of the quarter-final match on March 2, a glass bottle was thrown from a section of home fans situated in the south end of the East Stand towards Celtic winger Scott Sinclair, as he prepared to take a corner kick.
The Easter Road side issued a statement on Saturday after the match, vowing to try and identify any supporter involved in the disorder, but were unsuccessful in their bid to pinpoint those responsible.
Dempster told the club’s website: “We are heartened that several supporters have been in touch to try and identify the person responsible and we are following up on those.
“We know it can be difficult to challenge those adopting an aggressive manner during flashpoints but we would encourage people to get in touch and help us.”
Confirming that the club would be spending “no small amount” on overhauling the stadium’s CCTV set-up, Dempster added: “Clearly, this is money we would rather be spending on football.
“In future, there will be no hiding place for those who seek to tarnish the reputation of the vast majority who do Hibernian proud on a weekly basis at grounds all over the country.
“Any supporter caught engaging in behaviour that places players, staff and other fans at risk will be dealt with in the strongest possible terms available to us, whether that involves exclusion from Easter Road Stadium, a Football Banning Order or criminal prosecution when appropriate.”
Hibs have banned supporters in the past who have been involved in unacceptable conduct, with Dempster revealing that three fans had been excluded following the “use of pyrotechnic and another incident of disorderly conduct” during the club’s Ladbrokes Premiership match with Dundee at Dens Park.
She continued: “It is in all of our interests to ensure those spending their time and money to support Hibernian and grow the game in Scotland needn’t worry about the kind of environment they’re putting themselves in.
“We are proud of our supporters and the many, many positives they bring not only in a football sense but also to the wider community.
“I am determined that a mindless minority will not detract from that.”