The Sky Blues took a 3-0 lead in Northampton thanks to a double from Leon Clarke and a Callum Wilson strike, but two second-half goals from Lyle Taylor set up a nervous finish to the game for Pressley's men.
"We've now won our past two league games and move on to 10 points, which considering what we have been through, is a remarkable tally at this moment in time," PA quotes Pressley as saying.
"Credit to Sheffield United, I think that when you lose a manager you are always going to get a response from a group of players and finding themselves 3-0 down away from home, they had nothing to lose.
"After they got a bit of momentum we struggled to find our rhythm again and our passing again but saying that we had a couple of really good chances to kill the game off."
Coventry travel to Wolverhampton Wanderers next Saturday.