The Tigers needed to beat Town and hope Stoke lost at home to Leicester if they were to go up automatically, but the Potters' 0-0 draw would have denied Phil Brown's side even if they had not been beaten by Alan Lee's 70th-minute goal.
Lee scored less than a minute after coming on as a substitute, but Town's own faint play-off hopes were snuffed out as other results went against them.
The home side dominated and could have won more easily, as they hit the woodwork twice, had a goal wrongly disallowed, and a good penalty shout rejected.
Town had the ball in the net on three minutes when Shefki Kuqi nodded in after Pablo Counago's clever lob had hit the post, but he was incorrectly flagged offside.
Dean Marney and Bryan Hughes shot wide as Hull rallied, before Town hit the post again on 19 minutes with a low drive from Tommy Miller.
Alan Quinn twice failed to hit the target from good positions while Hull's growing frustration showed with three first-half bookings.
Quinn fired wide again for Town soon after the break, before Counago squandered a great chance, firing wide from eight yards after Owen Garvan's cross deflected into his path.
Quinn put two more efforts off target, Counago and Miller saw goalbound shots deflected wide and Jason De Vos nodded wide from a Garvan corner as Ipswich turned up the pressure.
They deservedly went ahead in the 70th minute when David Wright's free-kick was headed across goal by Lee to Jon Walters who returned it for Lee to angle his header into the corner.
Hull immediately produced their only effort on target in the game, when substitute Nicky Barmby headed powerfully into the arms of Stephen Bywater.
Ipswich had strong claims for a penalty when Sam Ricketts handled Danny Haynes' cross, but referee Andre Marriner ruled it accidental.
As Town sat back to defend their lead, Hull pressed with Marney shooting on to the roof of the net and Barmby volleying wide, but Ipswich held on comfortably.