Investigations are continuing into the ugly scenes that scarred Saturday's FA Cup semi-final defeat to Wigan at Wembley. Whilst the vast majority upheld a general improvement in behaviour from the Lions fans since the ugly days of the 1980s, 12 were arrested for their part in the disgraceful outbreaks of fighting.
Millwall have vowed to take the strongest action against those found to be responsible. But Jackett feels there is only so much the club can do, saying: "We will continue to work hard."
He added: "Whether we ever do it (get rid of the reputation) is a tough call. I have been here a number of years and am very proud of the way everyone has worked at the club.
"There has been a considerable amount done. The board of directors have worked in every direction they possibly can, making sure the players go out into their local community.
"It is a disappointing day."
Four police officers received minor injuries in the trouble, some of which was shown live on TV.
Two Wigan supporters were also arrested, although they were not involved in clashes with Millwall counterparts.
A Metropolitan Police spokesman said four of the arrests were for affray, one for affray and possession of Class A drugs, one for affray and assault on police, two for public order offences, one for assault causing actual bodily harm and possession of Class A drugs, one for a racially aggravated public order offence, one for ticket touting, one for possession of Class A drugs, one for theft and possession of offensive weapon, and one for breach of banning order.
The police spokesman said: "A number of lines of inquiry are being pursued. There will be a significant post-match review and further investigation will take place to identify those responsible for committing offences."