Colin Todd admitted that City's 2-2 comeback draw at Peterborough was not good enough.
Dean Windass took his goal tally to 21 with a second-half double to grab a point at London Road.
City remain five points adrift of the last play-off spot but Todd believed Saturday was a big missed opportunity.
"We should be coming to places like Peterborough and winning," he said. "The lads know that and you could smell the disappointment in the dressing room.
"A lot of teams would have caved in at two down so credit where it's due and we could have won it at the end. But, without being disrespectful, we should be winning games like that anyway."
Todd has set City a minimum target of six wins from the run-in and was confident of bagging one of those at second-from-bottom Posh.
But City were rocked by a rare slip from keeper Paul Henderson who allowed a long-range effort to slip through his hands.
Todd said: "It was an uncharacteristic mistake and that put us on the back foot. It was a straight-forward catch and you can't legislate for things like that.
"He's had one or two this season but it's about how he comes through it now.
"There is a lot going for us but we just have little lapses of concentration that cost us."
Windass rescued a draw with a stunning volley - a candidate for goal of the season.
Todd added: "You'll not see many better than that. It had a lot of class about it but that's typical of what the man can do.
"Never mind the Premiership, we should be raving about goals like that."
Next up are fifth-placed Hartlepool, who have lost four in a row. It's a game City must win.
Todd added: "There's always pressure on at this stage of the season. There would have been even if we had won. We need to beat Hartlepool, which would give us four points from the two games. But we'll still look back on this one.
"We know it's never going to be easy away from home but we made it really difficult for ourselves."
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