Playing in Northampton for the first time due to an ongoing dispute with the Ricoh Arena, the Sky Blues raced into a 3-0 half-time lead thanks to a Leon Clarke penalty and goals for Callum Wilson and Billy Daniels, his first senior strike.
But the Robins responded after the break as Sam Baldock scored twice, either side of Jay Emmanuel-Thomas' deflected free-kick, to level. Wilson put Coventry back in front a minute later with a close-range volley before Marvin Elliott equalised with a powerful strike from 12 yards in the 84th minute.
Daniels smashed in the decider from close-range in the 87th minute and the Sky Blues hung on to begin eating into their ten-point deduction.
Pressley said: "I am exceptionally proud of this group of players.
"In the first half especially, I thought we were outstanding, the level of some of our football and the intensity of our pressing game. We didn't allow Bristol City to get any control of the game and we looked such a threat on the counter attack.
"I was truly, truly proud of that first-half performance. I didn't think we played too badly in the second half.
"Obviously we conceded a couple of disappointing goals but they probably scored from all the opportunities they had and we just seem to be carrying no luck at the moment.
"The players deserve so much credit. When you are 3-0 up and you are pegged back, it is very easy to go under. But they didn't go under, they showed that unity and spirit that is so evident in our club at this moment in time."