They went close with a string of efforts, were denied by a brilliant save, saw a goal disallowed and had a penalty appeal turned down as they endured their third stalemate in four games.
Despite a nine-game unbeaten run, Ipswich remain entrenched in the bottom three, having only scored seven goals in that time.
The Irishman said: "I don't think we played that well but we had some good chances.
"The fact we didn't take them was very frustrating and I'm getting fed up of using that word.
"We've got to start putting the ball in the back of the net and I don't just mean my strikers - anyone.
"Peterborough put their bodies on the line but it's surprising me how much trouble we're having scoring goals.
"I need my players to step up to the plate and take a sniff of a chance.
"Instead of that, we always seemed to be on our heels last night."
Town thought they had broken the deadlock three minutes before the interval when Jon Walters delivered a raking cross for Stern John.
The loanee hung in the air and nodded the ball past Joe Lewis, only for referee Andy Hall to rule his goal out for pushing full-back Scott Griffiths.
Town were incensed and there was more frustration just after, when Damien Delaney's rising shot in the box appeared to hit Ryan Bennett's arm.
However, the official waved play on.
Asked about the first flashpoint, Keane said: "I always judge the reaction of both sets of players, but the one person who thought it was a foul was the referee."
Peterborough delivered a couple of timely reminders of their potency on the break.
Craig Mackail-Smith slid one chance wide of the post.
Then Lee Frecklington got on the end of Chris Whelpdale's cross but his header was brilliantly saved by Arran Lee-Barrett.
There was one last chance right at the end when Aaron McLean's drive was deflected just wide by Delaney.
Posh boss Mark Cooper said: "It was a very resolute performance.
"On Saturday we conceded a couple of needless goals but tonight the goalkeeper and centre-halves were outstanding.
"They had to deal with a lot of balls into the area but they won nearly every header.
"When they didn't they won the second ball that bounced on the edge of the box.
"I was very pleased defensively and, being greedy, we could have nicked it at the end.
"When you're in the position we're in and you come to a place like this, with the players they've got, you have to respect that.
"You can't go all-out attack. We tried to defend properly and play a bit on the counter-attack.
"That's three games unbeaten now and we have to build on this.
"We mustn't think we can just turn up and it'll happen for us at Coventry on Saturday, just because we've had some good performances.
"We've got to show the same work-rate and desire."