Gary Johnson said his side paid the price for not converting their chances, as City were held to a draw at home for the eleventh time this season.
After Nicky Maynard put the home side ahead with his eleventh goal of the season in the 69th minute, Preston defender Youl Mawene snatched an equaliser from a corner to leave City four points adrift of the play-offs.
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Match Report: Verdict from Ashton Gate
Gary told Bristol City World: "I thought we did enough to win the game. But that's been our problem this season - we've had too many draws at home where we have lacked that bit of concentration at times [and failed to convert our chances].
"We played some good football and so did they and it made for quite an open game.
"I thought the lads were up for it. We looked quite threatening on occasions and got our combination play going a little bit.
"I thought we created enough good chances to win the game but we just didn't tuck them away.
"We then made two mistakes - and when you put two mistakes together it normally costs you a goal at this level and that is what happened today."
Commenting on Preston's equaliser, which occurred after Bradley Orr surprisingly knocked a loose ball out for a corner when in plenty of space, Gary said: "Brad feels terrible - he didn't know why he kicked it out of play, but when you aren't under pressure you don't want be giving a corner away.
"Having said that, if you do give the corner away then you have to stay with your man.
"People are designated with men and if somebody gets in front of [them] and across [them], that's the man you need to chastise in your team who's not picking up.
"I thought we created enough good chances to win the game but we just didn't tuck them away."
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"Dele had a great game - and produced a great bit of play for the goal - but he's lost Mawene and it's cost us that particular goal.
"People have got to do better when they have a responsibility to mark from corners."
With five games left to play, the draw leaves City four points off sixth-placed Cardiff, who have three games in hand, starting with tomorrow morning's derby clash with Swansea.
And Gary refused to let the result draw a line under his side's play-off hopes ahead of the Easter weekend's double-header against Nottingham Forest (away) and Ipswich (home).
He said: "It's a better [result] for them than it is for us but we are not right out of it like we would have been had we lost.
"We'll wait and see how Cardiff get on tomorrow but we've certainly left ourselves with a little bit more to do.
"The Easter period always sorts the teams out. Generally, you know what you are competing for after the two games at Easter.
"We have to get two results and see where we are."