The hosts started strongly and Tommy Rowe should have done better when he found space on the edge of the area but he drilled his shot just wide of the target.
The Posh nearly paid for their lack of clinical edge when Aaron Cresswell fed Frank Nouble, who twisted and turned to fire a shot at goal which smacked the post and bounced clear.
After the break, Peterborough were on the attack straight away but Danny Swanson's deflected shot went just wide of the target.
Nouble was in the action for Ipswich and came so close to giving his side the lead but Posh keeper Robert Olejnik made the save to deny the striker.
Neither side could produce a winner as the game ended goalless.