"Club officials are working with police and the relevant authorities in scouring CCTV footage and photography - as well as ploughing through witness statements sent to the club by supporters - to identify culprits.
"Anyone found guilty of any disorder will face stringent action."
Club representatives met at St. Andrew's on Thursday morning with a further meeting set for next week involving Aston Villa, the local authority, safety advisory committee and the emergency services.
Acting Blues chairman Peter Pannu said: "We'll support the football authorities and police in this investigation.
"I promise there will be an impartial investigation by the club as we do not condone the embarrassing actions of certain individuals."
The FA has called on both clubs to impose the toughest available sanctions on fans, including banning orders.
The ugly scenes came on the eve of the vote to decide the hosts of the 2018 World Cup, and only time will tell if it affects England's chances.
"The whole of English football has worked hard to eradicate scenes of disorder from our game, with Home Office figures this week showing a significant drop in arrests at the many thousands of football matches held every week, the majority of which still pass trouble free," added the FA statement.
Birmingham boss Alex McLeish admitted the scenes were reminiscent of the violence that marred English football during the 1970s and 80s.
"It doesn't look good when you see them running on like that. It takes us back to the dark ages," said McLeish. "I'm disappointed. Fans shouldn't come on to the pitch. That's soured the win for us.
"I know they haven't beaten Villa for a while and our fans were treating it almost like a cup final, but when you see flares thrown from and into the crowd it is not something we want to be associated with at all."
However, McLeish dismissed that suggestions that it may have any affect on the World Cup vote in Zurich on Thursday.
"I don't think that it will affect the bid, I'm sure that's already decided, and let's hope England gets it, because it deserves it," said the Scot.
There has been a history of clashes between supporters of these two Midlands rivals, which has led to games being moved to early kick-offs following a request from local police.
The last time the two sides played in an evening game at Villa Park in 2002, there were several pitch invasions and ugly clashes between supporters before and after a bad-tempered game in which Villa's Dion Dublin and Joey Gudjonsson were sent off.
"Before the game there were lots of meetings with the police and all the players and management groups saying that the world was probably watching this game because of what's happening on Thursday, and I thought both sets of players did their job," said Aston Villa assistant manager Gary McAllister.
"I don't think it will affect England's World Cup bid. It is an outstanding candidate for this World Cup. Everything is in place and it is about time it came here."
Dozens of additional police had been hired for the match but they struggled to keep the sheer numbers of rioting fans in check and were unable to prevent flares being thrown, while Villa fans appeared to rip out seats and throw them back towards the pitch.
Zigic scored the winner for Birmingham with five minutes to go
Police eventually managed to gain control and shepherd the City fans off the pitch.
It was an ugly ending to what had been an enthralling encounter between the two sides.
Birmingham took the lead from the spot after Lee Bowyer was bundled over by Richard Dunne, with Sebastian Larsson firing home the resulting penalty.
Birmingham were denied a second when the linesman adjudged that Liam Ridgewell had been interfering in play after Nikola Zigic's shot had squirmed out of Villa keeper Brad Friedel's grasp and over the line.
In the next attack, Gabriel Agbonlahor side-footed his third goal in three games at St Andrew's to bring Villa level.
But, with five minutes remaining Zigic scored the winner via a defection off Villa defender Luke Young.
"I'm really proud of the players," said McLeish. "I felt we deserved it for our efforts over the game.
"You think decisions aren't going to go your way. And we could have been 2-0 up if the offside had gone our way. But we got our reward in the second half."
Birmingham now face West Ham in the semi-finals, with the first leg being played at Upton Park in week commencing 10 January before a return leg at St Andrew's in week commencing 24 January.
"When you get draws like that you think the second leg at home will be beneficial," claimed McLeish. "We need to go to West Ham and hope to get a score we can bring back to St Andrew's."
Birmingham have struggled for consistency this season and are only three points above the Premier League relegation zone with 17 points from 15 games.
Houllier 'hurting' after Cup exit
"A result like this lifts everybody and it is a chance to go to Wembley," added McLeish. "We always talk about the bread and butter of the league but we respect this competition and we would like to go the final.
"I had a good feeling about it. I'm delighted for them because they've met a lot of challenges over the last year and half. And they've kept rising to those challenges."
Villa boss Gerard Houllier felt the visitors were the better team, but errors cost them.
"I'm very disappointed for the fans and the players," said the Frenchman. "We were probably the better team overall and probably deserved more. But we made silly mistakes to cost us goals.
"We were stunned because I don't think the boys deserve to be out of the competition. We lacked some goals if we're honest but we can't score three goals every week."
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