The npower Championship side are aiming to cap a miserable week for Villa, who were humiliated in the Capital One Cup semi-final by Bradford on Tuesday night, by knocking them out of the FA Cup.
Paul Lambert's young side are also struggling in the Barclays Premier League and Millwall will be fancied to cause another upset under the lights at The Den.
But Jackett said: "In a cup tie like this we are the underdog. Up until recently their results had been very good, but lately the confidence seems to have gone out of the team. Maybe that's what you get with young players.
"But even if Villa were mid-table they would still see this as a tricky tie. Our responsibility is to put on a performance that justifies that and can lead a passionate crowd towards a good evening."
Captain Danny Shittu is in his second spell with Millwall and has first-hand experience of facing the hostile Den crowd as a member of the opposition.
"If the fans can get into them the way they got to me when I came back with QPR, I'm sure it will affect one or two of their players," he said.
"As a player, we try to block it out and it is hard. This would be the last place I'd want to come after a loss to Bradford."
Jackett's former club Swansea will meet Bradford at Wembley after beating Chelsea on Wednesday, a victory overshadowed by Eden Hazard's kick at ball boy Charlie Morgan.
Jackett knows the youngster and his father Martin from his time as Swans manager, but has ruled out any similar antics from the Den ball boys tonight.
"I don't think we have any ball boys over the age of four, so if they are going to lie on the ball I think they'd struggle," he said.
"I've tried to think of every angle and every way we can beat Aston Villa - but that one has not crossed my mind."