Millwall's hopes of progressing to the Carling Cup fourth round for the first time since 2006 were shot down by first-half goals from Tamas Priskin and Gareth McAuley.
Although Steve Morison's fine 62nd-minute finish handed The Lions a lifeline, they were unable to find a way through the Tractor Boys' rearguard for a second time as Roy Keane's side held on for victory.
"On the balance of play I felt we were unlucky to lose," said Kenny Jackett.
"There were some harsh lessons for us to learn because we gave away soft goals.
But there were a lot of good things to take from this because we created some decent chances. We have to get through this period and go again."
Den boss Kenny had been looking for an immediate response from his players following Saturday's home hammering by Watford, but he was forced to shuffle his playing pack with Jimmy Abdou ruled out through injury, and both Kevin Lisbie and Theo Robinson ineligible.
Starting with a 4-3-3 formation in which Morison spearheaded a three-pronged attack flanked by Danny Schofield and James Henry, it was The Lions who created the best of the early chances.
None more so than in the third minute when Henry's inviting ball from the right picked out the unmarked Morison. The flag stayed down but instead of glancing the ball into the back of the net, his header drifted agonisingly wide of a gaping goal.
Hackett went close with a low drive and then did well to keep the ball in play, slipping a pass to Alan Dunne whose delivery was headed into keeper Brian Murphy's hands by Morison.
Former Ipswich player Scott Barron twice provided good supporting runs on the overlap, but saw his first shot held and then whipped in an angled effort that flew just off target.
But it was Ipswich, who had barely had a look in until the 23rd-minute, who took the lead when Andros Townsend was allowed too much space to deliver from the left and Priskin's header looped over the outstretched hands of keeper David Forde.
Ipswich visibly grew in confidence with Townsend's drive flashing across the face of goal before the visitors added a second, deep into first-half injury-time.
There seemed little danger when Townsend whipped in a free-kick, McAuley stuck out a leg and the ball somehow crept under the arms of keeper Forde and squirmed over the line.
That should have been that, but a double substitution by Jackett just before the hour mark sparked just the reaction required.
On came Neil Harris and Darren Ward in a move that saw Barron switch to the left flank, Hackett to the right in a more orthadox 4-4-2 formation.
Just three minutes after the duo's introduction a deft forward pass by Tony Craig, playing his first competitive game since the Play-Off Final, picked out Morison in the danger zone. Millwall's joint top scorer pirouetted before slamming home to reduce the arrears and hand his side a much needed lifeline.
Spurred on by the Den faithful. who tried their best to get behind the team, Millwall were not left wanting in terms of effort and endeavour, but just lacked that final cutting edge where it mattered most.
Chopper's 72nd-minute curler was held by the keeper following good work by Tamika Mkandawire and Barron, whilst Trotter scooped over the bar from 18 yards after Morison and Barron had combined to create an opening.
The Lions had a decent opportunity to force extra time in the dying seconds when Barron's delicious delivery was met by Hackett, only for the midfielder to tamely glance his header inches post the post.
With that went Millwall's last real chance and and it is Ipswich who take their place in Saturday's fourth round draw.
Millwall: Forde, Dunne, Barron, Mkandawire, Robinson, Craig, Schofield (Ward, 58mins), Trotter, Morison, Hackett, Henry (Harris, 59mins). Subs not used: Mildenhall, Grabban, Grimes, Smith, Laird.
Bookings: Dunne (35mins), Trotter (70mins)
Scorer: Morison (62mins)
Ipswich Town: Murphy, Eastman, McAuley, Delaney, Kennedy, Hyam, Peters, Healy (Scotland, 54mins), Townsend (Leadbitter, 63mins), Priskin (Wickham, 64mins), Lambe. Subs not used: Fulop, Norris, Brown, Murray.
Booking: Wickham (88mins)
Scorers: Priskin (23mins), MacAuley (45+3mins)
Ref: Andy D'Urso
Att: 5,070 (away 799)