Kenny Jackett, sitting in his office at The Den, breaks into laughter as he thinks back to one of the more surreal moments of his managerial career. He was in charge of Swansea City, it was the final day of the 2004-05 season and the South Wales club had just defeated Bury at Gigg Lane to win promotion from the fourth tier. Just about everything had gone to plan until Jackett spotted Willy Guéret, the Swansea goalkeeper, being handcuffed and led off by police.

"We had been automatically promoted and the players went back into the dressing room but then there were thousands of Swansea supporters by the tunnel singing, so the players wanted to go back out to see them," the Millwall manager says, smiling. "They ended up going to an area where the safety stewards and the police weren't too happy and Willy was on top of somewhere deemed unsafe, so the police arrested him and took him down the station.

"Willy was a big lad and it took four of them to get him in the back of the van. But they did, with his full goalkeeper's kit on, and locked him up. So we got changed, I did the press, got on to the coach and had to go via the police station to get our goalkeeper because the players wouldn't go without him. I had to go into the station and get him. But I can still see the coppers trying to carry him off."

It is a story worth recalling because it provides a reminder of how far Swansea have come in such a short space of time and also highlights the part that Jackett played in the club's revival, which is recognised inside the Liberty Stadium but often overlooked by those outside. Huw Jenkins, the Swansea chairman, credits Jackett with laying the foundations for the club's magnificent rise through the divisions, which has culminated in a place in next month's League Cup final.

"It's certainly a different club now than the one we started out with [at the Vetch Field]," says Jackett, who was replaced by Roberto Martínez early in 2007, the season after Swansea had just missed out on back-to-back promotions when they lost to Barnsley on penalties in the play-off final. "You can't be at one club all the way through, you need somebody slightly different to take it on. But I'm very proud to have played my part in the development of a very good club."

Jackett's work at Millwall has also been impressive since his appointment in November 2007. Millwall won promotion from League One in his second full season in charge and are now ninth in the Championship, which is quite an achievement for a club with the third lowest gates in the division. "Our last three Championship attendances have been 9,000," Jackett says. "But the beauty of it is, if there's 9-10,000 at The Den, when you play well, that feels like 20,000. It is a hostile atmosphere when the team gets going."

Jackett, 51, hopes that will be the case on Friday night when Millwall take on Aston Villa in a fourth-round FA Cup tie that has the feel of an upset waiting to happen. Villa are fourth from bottom in the Premier League and on Tuesday night were dumped out of the Capital One Cup by Bradford City of League Two. Although Jackett makes it clear that he respects Villa, in particular their attacking players, he also senses the chance for a scalp.

"Can we exploit a Premier League club at home? I think we can," says Jackett, who still has his shirt and runners-up medal from the 1984 FA Cup final, when he was in the Watford side that lost to Everton. "We would like to think, on the right day, we can upset anyone at The Den. Millwall, generally, are a good underdog."

Set pieces should offer Millwall plenty of encouragement. All four Bradford goals across the two semi-final matches came via corners and Villa have conceded more times from dead-ball situations in the Premier League than any other club.

"I think set pieces are a big part of the game anyway," Jackett says. "It's not like something that's on the backburner and then suddenly for this game it comes to the fore. We've had good delivery on corners from James Henry, generally, and we haven't got on the end of enough, so it is something we are looking to improve on anyway. But, yes, if there is a weakness there, of course we will try to concentrate on it."

The five and a bit years Jackett has spent in charge of Millwall make him one of the longest-serving managers in the country and have also given him a strong emotional pull towards a club that has not been without its off-field problems in the past. "I think to some degree [the stigma] probably always will be there in some people's eyes but, when you work for Millwall, you realise what a terrific club it is," Jackett says. "It's an old-fashioned football club – very passionate, working-class and traditional. And I think that's a strength of the club."

There is certainly much to be admired about the way in which Millwall have backed a campaign to prevent the closure of the A&E department at nearby Lewisham hospital. The Millwall players will warm up for the Villa match wearing T-shirts in support of the hospital and the club have given hospital staff and campaigners permission to come to The Den prior to the game to hand out leaflets and collect signatures for a petition. "It's a close-knit community around here," Jackett says.

A Cup run would give everyone a lift while at the same time enabling Jackett to clock up a few more matches in his quest to reach four figures.

"I think I'm at around 500 [as a manager], I would love to be able to get to 1,000 – that's definitely an ambition of mine," he says. "To get to the top level is obviously an ambition – and I would love the opportunity to do that with Millwall – but I think longevity in management is a big achievement."