The Scottish champions issued life bans to three fans identified as being party to the lighting and throwing of flares and firecrackers before and during the live televised Scottish Cup fourth round tie against Stranraer at Stair Park on Sunday.
Police Scotland are investigating the use of pyrotechnics, along with alleged sectarian singing, while Scottish FA compliance officer Tony McGlennan is conducting his own review of the scenes.
The travelling Celtic fans will now be under close scrutiny in the Friday evening fixture against Dundee United which is being televised live through the UK by BT Sport.
Deila, who condemned the offenders immediately after the tie at Stranraer, has welcomed the club’s swift action along with statements from three of their main supporters’ groups which backed the stance taken by Celtic chief executive Peter Lawwell and his fellow directors.
The Celtic manager now hopes the law-abiding majority will help in the bid to end what has become a recurring issue for the club at home and in Europe over recent years.
“It’s important that as a group, everybody tries to get rid of it,” said Deila. “That’s not only the club, but the fans. It’s important that there is justice within the fans as well.
“This is something we want to get rid of. It’s not something we want to have on our reputation. We know 98 per cent of our fans are not supporting this kind of behaviour.
“There are two points to make - 98 per cent of our fans are fantastic and every club has problems, it’s not only Celtic. But when you have as many fans as we have, it’s tough to get it under control.
“But we need to do everything we can to make every stadium and arena we play at safe for everybody.
“I think the club’s statement and the action they took was very important. The consequences have to be there. If not, they will just do it again. So that was good action.
“It’s important we get away from the things that are hurting our reputation. There are a lot of clubs in the world with the same problem. It’s nothing new, but we have to take it seriously and we will do.”