Forest had taken the lead through Garath McCleary in the 31st minute and had dominated for long periods.
But Colin Calderwood was left to contemplate a ninth match without a win after referee Graham Laws pointed to the spot seven minutes into the second half, giving Tommy Miller the chance to level.
Forest had the ball in the back of the net after three minutes, but McCleary's close-range effort was ruled out with the winger having strayed offside.
A quick break from Andrew Cole set-up a second chance for McCleary, but this time he fired wide from the edge of the box.
New signing Lee Camp had shown a few confident touches for Forest - following his arrival on loan from QPR - but the keeper was relieved to see a superb 25-yard strike from Jon Walters bounce back off the bar and away.
A short spell of pressure did culminate in an opening goal, however, after a shot from Paul Anderson was saved at the expense of a corner.
Chris Cohen's curling delivery was then only half-cleared to the edge of the area from where McCleary placed a precise finish low into the corner of the net.
Twice in the space of a minute Camp had to race to the edge of the box to thwart Walters as he threatened to burst through on goal.
But the keeper was not to blame when Ipswich forced an equaliser in controversial fashion.
It seemed a generous decision when referee Laws pointed to the spot following Anderson's challenge on Alan Quinn, but Miller was in no mood for sympathy as he smashed the ball low into the bottom corner.
Forest had a penalty appeal of their own turned down after Gareth McAuley appeared to have hauled back Nathan Tyson in the box.
While substitute Lewis McGugan and Tyson both forced smart saves from Richard Wright and Wes Morgan planted a downward header wide from a glorious position.
But they could not find a way to edge their way back into the lead and still find themselves rooted to the foot of the table.